What is the integral from 0 to pi/4 of 2sec(x) ?

The integral from 0 to pi/4 of 2sec(x) is 2ln(1+sqrt(2))

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integral from 0 to pi/4 of 2sec(x)

\int_{0}^{\frac{π}{4}} 2 sec (x) d x

2 ln (1 + 2)

Decimal

1.76274 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 2 sec (x) d x

Take the constant out:

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

= 2 \cdot \int_{0}^{\frac{π}{4}} sec (x) d x

Use the common integral:

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= 2 [ln ∣ tan (x) + sec (x) ∣]_{0}^{\frac{π}{4}}

Compute the boundaries:

ln (1 + 2)

= 2 ln (1 + 2)

f^{^{'}} (x) = x^{2} e^{x^{2}}

\frac{3 x}{x + 1}

2 x^{2} - \frac{1}{16} ln (x)

\int cos^{3} (x) sin^{6} (x) d x

y = 8 i n^{x} + c

What is the integral from 0 to pi/4 of 2sec(x) ?
The integral from 0 to pi/4 of 2sec(x) is 2ln(1+sqrt(2))