What is the integral from 0 to x^2 of xcos(y) ?

The integral from 0 to x^2 of xcos(y) is xsin(x^2)

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integral from 0 to x^2 of xcos(y)

\int_{0}^{x^{2}} x cos (y) d y

x sin (x^{2})

Solution steps

\int_{0}^{x^{2}} x cos (y) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= x \cdot \int_{0}^{x^{2}} cos (y) d y

Use the common integral:

\int cos (y) d y = sin (y)

= x [sin (y)]_{0}^{x^{2}}

Compute the boundaries:

sin (x^{2})

= x sin (x^{2})

\int_{1}^{2} \frac{1}{1 + x ^{2}} d x

\int_{1}^{8} 5 d x

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

\int_{π}^{0} cos (x) d x

\int_{- 1}^{2} (3 u - 8) (u + 3) d u

What is the integral from 0 to x^2 of xcos(y) ?
The integral from 0 to x^2 of xcos(y) is xsin(x^2)