Definite Integration · Mathematics · Class 12

$$\int_\limits{-1}^1 \frac{|x-2|}{x-2} d x, x \neq 2 \text { is equal to: }$$

Assertion (A): $$\int_\limits2^8 \frac{\sqrt{10-x}}{\sqrt{x}+\sqrt{10-x}} d x=3$$ Reason (R): $$\int_\limits a^b f(x) d x=\int_a^b f(a+b-x) d x$$...

(a) Evaluate: $$\int_\limits0^{2 \pi} \frac{1}{1+e^{\sin x}} d x$$ OR $$\text { (b) Find: } \int \frac{x^4}{(x-1)\left(x^2+1\right)} d x$$...

Evaluate : $$\int_\limits0^{\frac{\pi}{2}} \sin 2 x \tan ^{-1}(\sin x) d x$$