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NCERT Class 12 Maths Chapter 7: Integrals 21 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 7 Integrals — Exercise 7.10

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

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

Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \frac{\sqrt{\sin{\left(x \right)}}}{\sqrt{\sin{\left(x \right)}} + \sqrt{\cos{\left(x…

Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \frac{\sin^{\frac{3}{2}}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)} +…

Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \frac{\cos^{5}{\left(x \right)}}{\sin^{5}{\left(x \right)} + \cos^{5}{\left(x \right)}}\…

Evaluate \(\int\limits_{-5}^{5} \left|{x + 2}\right|\, dx\) using definite-integral properties.

Evaluate \(\int\limits_{2}^{8} \left|{x - 5}\right|\, dx\) using definite-integral properties.

Evaluate \(\int\limits_{0}^{1} x \left(1 - x\right)^{n}\, dx\) using definite-integral properties.

Evaluate \(\int\limits_{0}^{\frac{\pi}{4}} \log{\left(\tan{\left(x \right)} + 1 \right)}\, dx\) using definite-integral properties.

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

Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \left(2 \log{\left(\sin{\left(x \right)} \right)} - \log{\left(\sin{\left(2 x \right)}…

Evaluate \(\int\limits_{- \frac{\pi}{2}}^{\frac{\pi}{2}} \sin^{2}{\left(x \right)}\, dx\) using definite-integral properties.

Evaluate \(\int\limits_{0}^{\pi} \frac{x}{\sin{\left(x \right)} + 1}\, dx\) using definite-integral properties.

Evaluate \(\int\limits_{- \frac{\pi}{2}}^{\frac{\pi}{2}} \sin^{7}{\left(x \right)}\, dx\) using definite-integral properties.

Evaluate \(\int\limits_{0}^{2 \pi} \cos^{5}{\left(x \right)}\, dx\) using definite-integral properties.

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

Evaluate \(\int\limits_{0}^{\pi} \log{\left(\cos{\left(x \right)} + 1 \right)}\, dx\) using definite-integral properties.

Evaluate \(\int\limits_{0}^{a} \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}}\, dx\) using definite-integral properties.

Evaluate \(\int\limits_{0}^{4} \left|{x - 1}\right|\, dx\) using definite-integral properties.

Show ∫₀ᵃf(x)g(x)dx=2∫₀ᵃf(x)dx if f(x)=f(a−x) and g(x)+g(a−x)=4.

Evaluate ∫₋π/₂^π/₂(x³+x cos x+tan⁵x+1)dx.

Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \log{\left(\frac{3 \sin{\left(x \right)} + 4}{3 \cos{\left(x \right)} + 4} \right)}\, dx\)…