Evaluate \(\int _{ 0 }^{ 50 }{ \left[ x-\left| x \right| \right] dx } \)

Evaluate \(\int _{ -2 }^{ 3 }{ \left| 1-{ x }^{ 2 } \right| } dx\)

Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { { cos }^{ 3/2 }x }{ { cos }^{ 3/2 }x+{ sin }^{ 3/2 }x } } dx\)

Evaluate \(\int_{0}^{\pi / 2} x \cos x d x\)

Evaluate \(\int_{0}^{1} \frac{d x}{\sqrt{1+x}-\sqrt{x}}\)

Evaluate \(\int_{1}^{3} \frac{1}{x(1+\log x)} d x\)

Evaluate \(\int_{0}^{2 \pi} \frac{1}{1+e^{\sin x}} d x\)

Evaluate \(\int_{0}^{a} \frac{\sqrt{x}}{\sqrt{x}+\sqrt{a-x}} d x\)

Evaluate \(\int_{0}^{\pi / 2} \frac{\tan ^{7} x}{\cot ^{7} x+\tan ^{7} x} d x\)

lf sin x, f(x) and cos x are in A.P, then find the value of \(\int\)f(x) dx.

Find the area of the region bounded y = x² - 5x + 4, x = 2, x = 3 and the x axis.

Find the volume of the solid generated when the region enclosed by y \(\mathrm{y}=\sqrt{x}\), y = 2 and x = 0 is revolved about the y axis.

Evaluate \(\int_{0}^{1} \log \left(\frac{1}{x}-1\right) d x\)

By using the properties of definite integrals, I evaluate \(\int_{0}^{1}|x-1| d x\)

Evaluate \(\int_{0}^{1} \frac{2 x}{1+x^{2}} d x\)