CBSE Class 12th Mathematics Chapter 7 - Integrals Important Questions with Answers

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Find ?\(\frac{\sec ^{2} x}{\sqrt{\tan ^{2} x+4}}\) dx. (Delhi 2019)

Question 2.

Find: ? \(\sqrt{1-\sin 2 x}\) dx, \(\frac{\pi}{4}\) < x < \(\frac{\pi}{2}\). (Delhi 2019)

Question 3.

Find: ? sin^-1 (2x) dx. (Delhi 2019)

Question 4.

Find the values of ?\(\frac{\tan ^{2} x \cdot \sec ^{2} x}{1-\tan ^{6} x}\) dx. (Delhi 2019)

Question 5.

Find the value of ? sin x ? log cos x dx. (Delhi 2019)

Question 6.

Find ? \(\sqrt{3-2 x-x^{2}}\) dx. (All India 2019)

Question 7.

Find ?\(\frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}\) dx. (All India 2019)

Question 8.

Find ?\(\frac{x-3}{(x-1)^{3}}\) e^x dx (All India 2019)

Question 9.

Find ?\(\frac{x-5}{(x-3)^{3}}\) e^x dx. (All India 2019)

Question 10.

Find: ?\(\frac{3 x+5}{x^{2}+3 x-18}\) dx. (Delhi 2019)

Question 1.

Find the value of ?\(\frac{\cos x}{(1+\sin x)(2+\sin x)}\) dx. (Delhi 2019)

Question 2.

Find ?\(\frac{x^{2}+x+1}{(x+2)\left(x^{2}+1\right)}\) dx. (All India 2019)

Question 3.

Find ?\(\frac{2 \cos x}{(1-\sin x)\left(2-\cos ^{2} x\right)}\) dx. (All India 2019)

Question 4.

Evaluate \(\int_{-1}^{2} \frac{|x|}{x}\) dx. (Delhi 2019)

Question 5.

Evaluate \(\int_{-1}^{2} \frac{|x|}{x}\) dx. (Delhi 2019)

Question 6.

Prove that \(\int_{0}^{a} f(x)\) dx = \(\int_{0}^{a} f(a-x)\) dx, hence evaluate \(\int_{0}^{\pi} \frac{x \sin x}{1+\cos ^{2} x}\). (Delhi 2019)

Question 7.

Prove that \(\int_{0}^{a} f(x)\) dx = \(\int_{0}^{a} f(a-x)\) dx. and hence evaluate \(\int_{0}^{\pi / 2} \frac{x}{\sin x+\cos x}\) dx. (All India 2019)