What is the integral from 0 to 1 of cos(sqrt(x)) ?

The integral from 0 to 1 of cos(sqrt(x)) is 2(sin(1)+cos(1)-1)

Popular >

integral from 0 to 1 of cos(sqrt(x))

\int_{0}^{1} cos (x) d x

2 (sin (1) + cos (1) - 1)

Decimal Notation

0.76354 \dots

Solution steps

\int_{0}^{1} cos (x) d x

Apply u-substitution

: \int_{0}^{1} cos (u) \cdot 2 u d u

= \int_{0}^{1} cos (u) \cdot 2 u d u

Take the constant out:

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

= 2 \cdot \int_{0}^{1} cos (u) u d u

Apply Integration By Parts

: [u sin (u) - \int sin (u) d u]_{0}^{1}

= 2 [u sin (u) - \int sin (u) d u]_{0}^{1}

\int sin (u) d u = - cos (u)

= 2 [u sin (u) - (- cos (u))]_{0}^{1}

Simplify

= 2 [u sin (u) + cos (u)]_{0}^{1}

Compute the boundaries:

sin (1) + cos (1) - 1

= 2 (sin (1) + cos (1) - 1)

\int_{1}^{e} \frac{2 ln ( x )}{x} d x

\int_{0}^{c o t (x)} \frac{1}{1 + t ^{2}} d t

\int_{0}^{\frac{1}{2}} x^{3} arctan (x) d x

\int_{1}^{2} y sin (x y) d x

\int_{0}^{1} 9 cos (\frac{π x}{2}) d x

What is the integral from 0 to 1 of cos(sqrt(x)) ?
The integral from 0 to 1 of cos(sqrt(x)) is 2(sin(1)+cos(1)-1)