What is the integral from 0 to 3/10 of 1/(100x^2+9) ?

The integral from 0 to 3/10 of 1/(100x^2+9) is pi/(120)

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integral from 0 to 3/10 of 1/(100x^2+9)

\int_{0}^{\frac{3}{10}} \frac{1}{100 x ^{2} + 9} d x

\frac{π}{120}

Decimal

0.02617 \dots

Solution steps

\int_{0}^{\frac{3}{10}} \frac{1}{100 x ^{2} + 9} d x

Apply Integral Substitution

= \int_{0}^{1} \frac{1}{30 ( u ^{2} + 1 )} d u

Take the constant out:

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

= \frac{1}{30} \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)

= \frac{1}{30} [arctan (u)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= \frac{1}{30} \cdot \frac{π}{4}

Simplify

= \frac{π}{120}

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\int_{3}^{9} \frac{2}{11 - 4 x} d x

\int_{4}^{\infty} \frac{1}{3 x - 10} d x

What is the integral from 0 to 3/10 of 1/(100x^2+9) ?
The integral from 0 to 3/10 of 1/(100x^2+9) is pi/(120)