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

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

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

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

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

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

Apply Trigonometric Substitution

: \int_{0}^{\frac{π}{2}} 1 d u

= \int_{0}^{\frac{π}{2}} 1 d u

Integral of a constant:

\int a d x = a x

= [1 \cdot u]_{0}^{\frac{π}{2}}

Simplify

= [u]_{0}^{\frac{π}{2}}

Compute the boundaries:

\frac{π}{2}

= \frac{π}{2}

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\int_{0}^{3} (5 x^{2} + 9 x) d x

\int_{\frac{π}{6}}^{\frac{π}{3}} csc (x) d x

\int_{1}^{3 x^{2}} \frac{sin ( t )}{t} d t

\int_{0}^{2 a} 2 a y d y

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