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NCERT Class 12 Maths Chapter 7: Integrals 22 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 7 Integrals — Exercise 7.8

Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.

Evaluate \(\int\limits_{-1}^{1} \left(x + 1\right)\, dx\).

Evaluate \(\int\limits_{2}^{3} \frac{1}{x}\, dx\).

Evaluate \(\int\limits_{1}^{2} \left(4 x^{3} - 5 x^{2} + 6 x + 9\right)\, dx\).

Evaluate \(\int\limits_{0}^{\frac{\pi}{4}} \sin{\left(2 x \right)}\, dx\).

Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \cos{\left(2 x \right)}\, dx\).

Evaluate \(\int\limits_{4}^{5} e^{x}\, dx\).

Evaluate \(\int\limits_{0}^{\frac{\pi}{4}} \tan{\left(x \right)}\, dx\).

Evaluate \(\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{4}} \csc{\left(x \right)}\, dx\).

Evaluate \(\int\limits_{0}^{1} \frac{1}{\sqrt{1 - x^{2}}}\, dx\).

Evaluate \(\int\limits_{0}^{1} \frac{1}{x^{2} + 1}\, dx\).

Evaluate \(\int\limits_{2}^{3} \frac{1}{x^{2} - 1}\, dx\).

Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \cos^{2}{\left(x \right)}\, dx\).

Evaluate \(\int\limits_{2}^{3} \frac{x}{x^{2} + 1}\, dx\).

Evaluate \(\int\limits_{0}^{1} \frac{2 x + 3}{5 x^{2} + 1}\, dx\).

Evaluate \(\int\limits_{0}^{1} x e^{x^{2}}\, dx\).

Evaluate \(\int\limits_{1}^{2} \frac{5 x}{x^{2} + 4 x + 3}\, dx\).

Evaluate \(\int\limits_{0}^{\frac{\pi}{4}} \left(x^{3} + 2 \sec^{2}{\left(x \right)} + 2\right)\, dx\).

Evaluate \(\int\limits_{0}^{\pi} \left(\sin^{2}{\left(\frac{x}{2} \right)} - \cos^{2}{\left(\frac{x}{2} \right)}\right)\, dx\).

Evaluate \(\int\limits_{0}^{2} \frac{6 x + 3}{x^{2} + 4}\, dx\).

Evaluate \(\int\limits_{0}^{1} \left(x e^{x} + \sin{\left(\frac{\pi x}{4} \right)}\right)\, dx\).

Evaluate \(\int\limits_{1}^{\sqrt{3}} \frac{1}{x^{2} + 1}\, dx\).

Evaluate \(\int\limits_{0}^{\frac{2}{3}} \frac{1}{9 x^{2} + 4}\, dx\).