What is the integral from 0 to t of 9/(sqrt(1-x^2)) ?

The integral from 0 to t of 9/(sqrt(1-x^2)) is 9arcsin(t)

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integral from 0 to t of 9/(sqrt(1-x^2))

\int_{0}^{t} \frac{9}{1 - x ^{2}} d x

9 arcsin (t)

Solution steps

\int_{0}^{t} \frac{9}{1 - x ^{2}} d x

Take the constant out:

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

= 9 \cdot \int_{0}^{t} \frac{1}{1 - x ^{2}} d x

Use the common integral:

\int \frac{1}{1 - x ^{2}} d x = arcsin (x)

= 9 [arcsin (x)]_{0}^{t}

Compute the boundaries:

arcsin (t)

= 9 arcsin (t)

What is the integral from 0 to t of 9/(sqrt(1-x^2)) ?
The integral from 0 to t of 9/(sqrt(1-x^2)) is 9arcsin(t)