What is the integral from 0 to 1 of 3/(sqrt(4-x^2)) ?

The integral from 0 to 1 of 3/(sqrt(4-x^2)) is pi/2

Popular >

integral from 0 to 1 of 3/(sqrt(4-x^2))

\int_{0}^{1} \frac{3}{4 - x ^{2}} d x

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{0}^{1} \frac{3}{4 - x ^{2}} d x

Take the constant out:

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

= 3 \cdot \int_{0}^{1} \frac{1}{4 - x ^{2}} d x

Apply Trigonometric Substitution

: \int_{0}^{\frac{π}{6}} 1 d u

= 3 \cdot \int_{0}^{\frac{π}{6}} 1 d u

Integral of a constant:

\int a d x = a x

= 3 [1 \cdot u]_{0}^{\frac{π}{6}}

Simplify

= 3 [u]_{0}^{\frac{π}{6}}

Compute the boundaries:

\frac{π}{6}

= 3 \cdot \frac{π}{6}

Simplify

= \frac{π}{2}

f (x) = \frac{x - 3}{x + 4}

\frac{s}{s ^{2} + 3}

\int 5 tan^{5} (x) d x

t^{2} - 4 t + 4

x d x + y d y = x y (x d y - y d x)

What is the integral from 0 to 1 of 3/(sqrt(4-x^2)) ?
The integral from 0 to 1 of 3/(sqrt(4-x^2)) is pi/2