What is the integral from-1 to 1 of 7/(1+49x^2) ?

The integral from-1 to 1 of 7/(1+49x^2) is 2arctan(7)

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integral from-1 to 1 of 7/(1+49x^2)

\int_{- 1}^{1} \frac{7}{1 + 49 x ^{2}} d x

2 arctan (7)

Decimal

2.85779 \dots

Solution steps

\int_{- 1}^{1} \frac{7}{1 + 49 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_{- 1}^{1} \frac{1}{1 + 49 x ^{2}} d x

Apply Integral Substitution

= 7 \cdot \int_{- 7}^{7} \frac{1}{7 ( 1 + u ^{2} )} d u

Take the constant out:

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

= 7 \cdot \frac{1}{7} \cdot \int_{- 7}^{7} \frac{1}{1 + u ^{2}} d u

Use the common integral:

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

= 7 \cdot \frac{1}{7} [arctan (u)]_{- 7}^{7}

Simplify

7 \cdot \frac{1}{7} [arctan (u)]_{- 7}^{7} : [arctan (u)]_{- 7}^{7}

= [arctan (u)]_{- 7}^{7}

Compute the boundaries:

2 arctan (7)

= 2 arctan (7)

What is the integral from-1 to 1 of 7/(1+49x^2) ?
The integral from-1 to 1 of 7/(1+49x^2) is 2arctan(7)