Maths MCQs for Class 12 with Answers Chapter 7 Integrals

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 7 Integrals. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Integrals MCQs Pdf with Answers to know their preparation level.

Integrals Class 12 Maths MCQs Pdf

Question 1.
\(\int_{1}^{2} x^{2} d x\)
(a) 1
(b) \(\frac{7}{3}\)
(c) \(\frac{1}{3}\)
(d) 0
Answer:
(b) \(\frac{7}{3}\)

Question 2.
\(\int_{0}^{2}\left(x^{2}+3\right) d x\)
(a) \(\frac{25}{3}\)
(b) \(\frac{26}{3}\)
(c) \(\frac{24}{3}\)
(d) None of these
Answer:
(b) \(\frac{26}{3}\)

Question 3.
Evaluate: \(\int_{0}^{\pi / 4} \sqrt{1-\sin 2 x} d x\)
(a) √2 – 1
(b) √2 + 1
(c) √2
(d) None of these
Answer:
(a) √2 – 1

Question 4.
Evaluate: \(\int_{0}^{2 \pi} \sin \left(\frac{\pi}{4}+\frac{x}{2}\right) d x\)
(a) -2√2
(b) -2
(c) √2
(d) 2√2
Answer:
(d) 2√2

Question 5.
Evaluate: \(\int_{1}^{2} \frac{d x}{x^{2}}\)
(a) \(\frac{1}{2}\)
(b) 1
(c) 2
(d) -1
Answer:
(a) \(\frac{1}{2}\)

Question 6.
Evaluate: \(\int_{0}^{1} \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x\)
(a) \(\frac{\pi}{2}\) – log2
(b) π
(c) \(\frac{\pi}{4}\)
(d) \(\frac{\pi}{2}\) – log2
Answer:
(a) \(\frac{\pi}{2}\) – log2

Question 7.

Answer:
(a) \(\log \left(\frac{4}{3}\right)\)

Question 8.

Answer:
(c) \(\frac{4-\pi}{4 \sqrt{2}}\)

Question 9.

Answer:
(c) \(\frac{2}{\sqrt{5}} \tan ^{-1}\left(\frac{1}{\sqrt{5}}\right)\)

Question 10.

Answer:
(c) \(\frac{1}{\sqrt{5}} \log \left(\frac{3+\sqrt{5}}{2}\right)\)

Question 11.
Evaluate: ∫(2tan x – 3cot x)² dx
(a) -4tan x – 9cot x – 25x + C
(b) 4tan x – 9cot x – 25x + C
(c) -4tan x + 9 cot x + 25x + C
(d) 4tan x + 9cot x + 25x + C
Answer:
(b) 4tan x – 9cot x – 25x + C

Question 12.

Answer:
(a) \(\frac{a^{x}}{\log a}+\frac{x^{a+1}}{a+1}+a^{a} x+C\)

Question 13.

Answer:
(a) \(-\frac{1}{4} \tan (7-4 x)+C\)

Question 14.

Answer:
(a) \(\frac{1}{(\log 2)^{3}} 2^{2^{2^{x}}}+C\)

Question 15.

Answer:
(b) \(-\frac{\cos ^{4} x}{4}+C\)

Question 16.

Answer:
(a) \(\frac{-3}{\sqrt[3]{\sin x}}+C\)

Question 17.
Evaluate: ∫tan(x – θ) tan(x + θ) tan2x dx
(a) \(\frac { 1 }{ 2 }\) log|cos2x| – log|cos(x – θ)| + log|cos(x + θ)| + C
(b) –\(\frac { 1 }{ 2 }\) log|cos2x| + log|cos(x – θ)| + log|cos (x + θ)| + C
(c) –\(\frac { 1 }{ 2 }\) log|cos2x| – log|cos(x – θ)| – log|cos(x + θ)| + C
(d) None of these
Answer:
(b) –\(\frac { 1 }{ 2 }\) log|cos2x| + log|cos(x – θ)| + log|cos (x + θ)| + C

Question 18.

Answer:
(b) \(-\frac{2}{\sqrt{\tan x}}+\frac{2}{3}(\tan x)^{3 / 2}+C\)

Question 19.

Answer:
(b) \(-\frac{3}{5} \tan ^{-5 / 3} x+3 \tan ^{1 / 3} x+C\)

Question 20.

Answer:
(c) \(\frac{1}{4} \log \left|x^{4}-9\right|-\frac{1}{12}\left|\frac{x^{2}-3}{x^{2}+3}\right|+C\)

Question 21.

Answer:
(a) \(\frac{\pi}{2}\)

Question 22.

Answer:
(a) \(\frac{8}{21}\)

Question 23.

Answer:
(a) 2 – √2

Question 24.

Answer:
(b) \(\frac{1}{2}+\frac{1}{\pi+2}-A\)

Question 25.

Answer:
(d) \(\frac{\pi}{2}\)

Question 26.

Answer:
(c) π²

Question 27.

Answer:
(c) cosec(b-a) \(\log \left|\frac{\sin (x-b)}{\sin (x-a)}\right|\) + C

Question 28.

Answer:
(a) \(\frac{e^{x}}{1+x^{2}}+C\)

Question 29.

Answer:
(d) \(x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-\log |1+x|+C\)

Question 30.

Answer:
(d) a = \(\frac{1}{3}\), b = -1

Question 31.

Answer:
(a) 1

Question 32.

Answer:
(b) \(-\log \left|e^{-x}+\sqrt{e^{-2 x}-1}\right|+C\)

Question 33.

Answer:
(b) \(\frac{1}{n} \log \left|\frac{x^{n}}{x^{n}+1}\right|+C\)

Question 34.

Answer:
(c) \(\frac{1}{6} \tan ^{-1}\left(\frac{2 \tan x}{3}\right)+C\)

Question 35.

Answer:
(c) \(2 \sqrt{x}-3(\sqrt[3]{x})+6(\sqrt[6]{x})-6 \log (\sqrt[6]{x}+1)+C\)

Question 36.

Answer:
(b) \(\begin{array}{l}
-\frac{1}{3} \log |1+\tan \theta|+\frac{1}{6} \log \left|\tan ^{2} \theta-\tan \theta+1\right| \\ \quad+\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \tan \theta-1}{\sqrt{3}}\right)+C
\end{array}\)

Question 37.

Answer:
(a) \(\log |\sec x+\tan x|-2 \tan (x / 2)+C\)

Question 38.

Answer:
(c) \(\tan \frac{x}{2}\)

Question 39.

Answer:
(a) \(\frac{e^{x} \cos x}{1+\sin x}+C\)

Question 40.

Answer:
(b) \(e^{x}\left(\frac{x+2}{x+4}\right)+C\)

Question 41.

Answer:
(b) \(\begin{aligned} \frac{1}{2}(x+1) \sqrt{x^{2}+2 x+5} & \\ +2 \log |(x+1)+\sqrt{x^{2}+2 x+5}|+C & \end{aligned}\)

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