What is the integral from 0 to x^2 of 4xcos(y) ?

The integral from 0 to x^2 of 4xcos(y) is 4xsin(x^2)

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integral from 0 to x^2 of 4xcos(y)

\int_{0}^{x^{2}} 4 x cos (y) d y

4 x sin (x^{2})

Solution steps

\int_{0}^{x^{2}} 4 x cos (y) d y

Take the constant out:

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

= 4 x \cdot \int_{0}^{x^{2}} cos (y) d y

Use the common integral:

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

= 4 x [sin (y)]_{0}^{x^{2}}

Compute the boundaries:

sin (x^{2})

= 4 x sin (x^{2})

\int_{- \frac{π}{4}}^{\frac{π}{4}} 6 tan^{4} (x) d x

\int_{1}^{0} 6 x (4 - x) d x

\int_{0}^{2} 4 - t^{4} d t

\int_{1}^{11} 9 x^{- 2} d x

\int_{0}^{2} (6 x - 6) (8 x^{2} + 9) d x

What is the integral from 0 to x^2 of 4xcos(y) ?
The integral from 0 to x^2 of 4xcos(y) is 4xsin(x^2)