Integrals Class 12 Mathematics Important Questions

Important Questions Class 12

Please refer to Integrals Class 12 Mathematics Important Questions with solutions provided below. These questions and answers have been provided for Class 12 Mathematics based on the latest syllabus and examination guidelines issued by CBSE, NCERT, and KVS. Students should learn these problem solutions as it will help them to gain more marks in examinations. We have provided Important Questions for Class 12 Mathematics for all chapters in your book. These Board exam questions have been designed by expert teachers of Standard 12.

Class 12 Mathematics Important Questions Integrals

Very Short Answer Type Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

Question. Write the value of ∫sec x(sec x + tan x)dx
Answer. ∫sec x (sec x + tan x)dx
=∫(sec2 x + sec x tan x)dx = tan x + sec x + C

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

Question. Write the value of ∫2x dx
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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions
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Integrals Class 12 Mathematics Important Questions

Question. Evaluate : ∫x log 2x dx.
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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

∴ By second fundamental theorem of integral calculus, we have

Integrals Class 12 Mathematics Important Questions

Question. Given ∫ex (tan x +1)secx dx = ex f (x) + c Write f(x) satisfying above.
Answer. Given : ∫ex (tanx +1)secx dx = ex f(x) + C …(1)
L.H.S. = ∫ex (tanx +1)secx dx
= ∫ex (secx + secx tanx)dx
= ∫ex secx dx + ∫ex secx tanx dx
(Integrating first integral by parts)
= ex secx −∫ex sec x tan x dx +∫ex secx tanx dx +C
= ex sec x + C = ex f(x) + C (by (1))
On comparing, we get f(x) = sec x

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Integrals Class 12 Mathematics Important Questions

Answer. By the first fundamental theorem of integral calculus

Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

Question. Evaluate : ∫sec2(7 − 4x)dx
Answer.
Let I = ∫sec2(7 − 4x)dx

Integrals Class 12 Mathematics Important Questions

Question. Evaluate : ∫cos4x cos3xdx
Answer. Let I = ∫cos4x cos3xdx

Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

Short Answer Type Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions
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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions
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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions
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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions
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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

Question. Evaluate : ∫(| x | + | x − 2 | + | x − 4 |)dx
Answer. Let I = ∫(| x | + | x − 2 | + | x − 4 |)dx

Integrals Class 12 Mathematics Important Questions

Question. Evaluate : ∫[| x − 2 | + | x − 3| + | x − 5|]dx

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Integrals Class 12 Mathematics Important Questions

Question. Evaluate : ∫[| x −1| + | x − 2 | + | x − 3|]dx

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Integrals Class 12 Mathematics Important Questions
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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions
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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions
Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

Integrating by parts, taking (tan t sec2 t) as 2nd function.

Integrals Class 12 Mathematics Important Questions
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Integrals Class 12 Mathematics Important Questions
Integrals Class 12 Mathematics Important Questions
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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions
Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions
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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions
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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions
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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

Question. Evaluate : ∫e2x – sin(3x +1)dx

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Integrals Class 12 Mathematics Important Questions
Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions

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Integrals Class 12 Mathematics Important Questions
Integrals Class 12 Mathematics Important Questions
Integrals Class 12 Mathematics Important Questions

Long Answer Type Questions

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Answer. We have, by definition.

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Answer. We have by definition,

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Answer. We have, by definition

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Answer. We have, by definition

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Answer. We have, by definition

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Answer. We have, by definition