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

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}^{1} \frac{1}{1 - 4 x ^{2}} d x

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

\int_{0}^{3} \frac{1}{4 - x} d x

\int_{- 6}^{5} ∣ x ∣ d x

\int_{0}^{1} - 2 x^{2} + 2 x 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