What is the integral from 1 to 2 of 1/(xsqrt(x-1)) ?

The integral from 1 to 2 of 1/(xsqrt(x-1)) is pi/2

Popular >

integral from 1 to 2 of 1/(xsqrt(x-1))

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

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

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

Apply u-substitution

: \int_{0}^{1} \frac{2}{u ^{2} + 1} d u

= \int_{0}^{1} \frac{2}{u ^{2} + 1} d u

Take the constant out:

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

= 2 \cdot \int_{0}^{1} \frac{1}{u ^{2} + 1} d u

Use the common integral:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= 2 [arctan (u)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= 2 \cdot \frac{π}{4}

Simplify

= \frac{π}{2}

\int_{- 3}^{2} \frac{2 x}{x ^{2} + 5} d x

\int_{- π}^{π} x^{3} cos (x) d x

\int_{0}^{\frac{π}{2}} 5 sin (\frac{x}{2}) d x

\int_{0}^{π} x^{2} \cdot cos (n x) d x

\int_{0}^{x^{2}} cos (x^{2}) d x

What is the integral from 1 to 2 of 1/(xsqrt(x-1)) ?
The integral from 1 to 2 of 1/(xsqrt(x-1)) is pi/2