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_{0}^{2} y d y

\int_{- 1}^{1} x e^{x^{8}} d x

\int_{0}^{1} \frac{e ^{x}}{e ^{x} - 1} d x

\int_{0}^{\frac{π}{4}} cos^{2} (3 x) d x

\int_{0}^{t a n (x)} e^{- t^{2}} d t

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