What is the integral from 0 to x of sin(sqrt(t)) ?

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

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integral from 0 to x of sin(sqrt(t))

\int_{0}^{x} sin (t) d t

2 (sin (x) - x cos (x))

Solution steps

\int_{0}^{x} sin (t) d t

Apply u-substitution

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

= \int_{0}^{x} sin (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}^{x} sin (u) u d u

Apply Integration By Parts

: [- u cos (u) - \int - cos (u) d u]_{0}^{x}

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

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

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

Simplify

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

Compute the boundaries:

sin (x) - x cos (x)

= 2 (sin (x) - x cos (x))

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\int_{0}^{6} \frac{300}{3 Q + 2} d Q

\int_{1}^{e} \frac{e ^{l n (x)}}{x} d x

\int_{1}^{4} (x + 2 - x^{2}) d x

\int_{- 1}^{0} (x + 1)^{10} x d x

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