What is the integral from 0 to 1 of 7/(sqrt(1-x^2)) ?

The integral from 0 to 1 of 7/(sqrt(1-x^2)) is (7pi)/2

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integral from 0 to 1 of 7/(sqrt(1-x^2))

\int_{0}^{1} \frac{7}{1 - x ^{2}} d x

\frac{7 π}{2}

Decimal

10.99557 \dots

Solution steps

\int_{0}^{1} \frac{7}{1 - x ^{2}} d x

Take the constant out:

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

= 7 \cdot \int_{0}^{1} \frac{1}{1 - x ^{2}} d x

Use the common integral:

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

= 7 [arcsin (x)]_{0}^{1}

Compute the boundaries:

\frac{π}{2}

= 7 \cdot \frac{π}{2}

Simplify

= \frac{7 π}{2}

\int_{1}^{4} 5 \frac{ln ( x )}{x ^{2}} d x

y = 5 sec (5 x)

(5.6) (5.9)

y = 3 x^{2} - x^{3}

(x + y)^{2} d x + (x + y)^{2} d y = 0

What is the integral from 0 to 1 of 7/(sqrt(1-x^2)) ?
The integral from 0 to 1 of 7/(sqrt(1-x^2)) is (7pi)/2