What is the integral from-pi/4 to (3pi)/4 of sin(x) ?

The integral from-pi/4 to (3pi)/4 of sin(x) is square root of 2

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integral from-pi/4 to (3pi)/4 of sin(x)

\int_{- \frac{π}{4}}^{\frac{3 π}{4}} sin (x) d x

2

Decimal Notation

1.41421 \dots

Solution steps

\int_{- \frac{π}{4}}^{\frac{3 π}{4}} sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= [- cos (x)]_{- \frac{π}{4}}^{\frac{3 π}{4}}

Compute the boundaries:

2

= 2

\int_{0}^{4} 5 x + x d x

\int_{0}^{10} e^{- x} d x

\int_{1}^{3} - \frac{7}{x ^{2}} d x

\int_{0}^{α} x \cdot \frac{α}{x ^{α + 1}} d x

\int_{0}^{\infty} \frac{5}{x ^{2} + 3} d x

What is the integral from-pi/4 to (3pi)/4 of sin(x) ?
The integral from-pi/4 to (3pi)/4 of sin(x) is square root of 2