What is the integral from 0 to arcsin(x) of (cos(t)) ?

The integral from 0 to arcsin(x) of (cos(t)) is x

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integral from 0 to arcsin(x) of (cos(t))

\int_{0}^{a r c s i n (x)} (cos (t)) d t

x

Solution steps

\int_{0}^{a r c s i n (x)} cos (t) d t

Use the common integral:

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

= [sin (t)]_{0}^{a r c s i n (x)}

Compute the boundaries:

x

= x

\int_{- \frac{π}{2}}^{\frac{π}{2}} I n (cos (x)) d x

\int_{1}^{9} 10 u d u

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

\int_{0}^{10} \frac{x}{16 + 2 x} d x

\int_{- 13}^{2} \frac{1}{3 - x} d x

What is the integral from 0 to arcsin(x) of (cos(t)) ?
The integral from 0 to arcsin(x) of (cos(t)) is x