What is the integral from 0 to 4 of cos(sqrt(x)) ?

The integral from 0 to 4 of cos(sqrt(x)) is 2(2sin(2)+cos(2)-1)

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integral from 0 to 4 of cos(sqrt(x))

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

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

Decimal Notation

0.80489 \dots

Solution steps

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

Apply u-substitution

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

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

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

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

h \to 1 lim (\frac{e ^{h} - 1}{h})

y = - 4 x^{2}, (- 2, - 16)

2 x^{3} + 2 y^{3} - 9 x y = 0, (2, 1)

\int_{0}^{\infty} \frac{ln ( x )}{x} d x

\frac{d}{d x} (e^{6 x s i n (2 x)})

What is the integral from 0 to 4 of cos(sqrt(x)) ?
The integral from 0 to 4 of cos(sqrt(x)) is 2(2sin(2)+cos(2)-1)