Solve \int _0^{\pi /2} \int _0^x x sin y dy dx

Question

Evaluate the integral

\frac{π ^{2} - 4 π + 8}{8}

Alternative Form

\approx 0.662904

Evaluate

\int_{0}^{\frac{π}{2}} \int_{0}^{x} x sin (y) d y d x

To evaluate the iterated inter,first evaluate the inner integral

More Steps

\int_{0}^{\frac{π}{2}} (- x cos (x) + x) d x

Evaluate the integral

\int (- x cos (x) + x) d x

Use the property of integral \int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int - x cos (x) d x + \int x d x

Evaluate the integral

More Steps

- x sin (x) - cos (x) + \int x d x

Evaluate the integral

More Steps

- x sin (x) - cos (x) + \frac{x ^{2}}{2}

Return the limits

(- x sin (x) - cos (x) + \frac{x ^{2}}{2})_{0}^{\frac{π}{2}}

Solution

More Steps

\frac{π ^{2} - 4 π + 8}{8}

Alternative Form

\approx 0.662904

Show Solution