What is the integral from 0 to 1 of 7cos((pit)/2) ?

The integral from 0 to 1 of 7cos((pit)/2) is (14)/pi

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integral from 0 to 1 of 7cos((pit)/2)

\int_{0}^{1} 7 cos (\frac{π t}{2}) d t

\frac{14}{π}

Decimal

4.45633 \dots

Solution steps

\int_{0}^{1} 7 cos (\frac{π t}{2}) d t

Take the constant out:

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

= 7 \cdot \int_{0}^{1} cos (\frac{π t}{2}) d t

Apply u-substitution

: \int_{0}^{\frac{π}{2}} cos (u) \frac{2}{π} d u

= 7 \cdot \int_{0}^{\frac{π}{2}} cos (u) \frac{2}{π} d u

Take the constant out:

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

= 7 \cdot \frac{2}{π} \cdot \int_{0}^{\frac{π}{2}} cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= 7 \cdot \frac{2}{π} [sin (u)]_{0}^{\frac{π}{2}}

Simplify

7 \cdot \frac{2}{π} [sin (u)]_{0}^{\frac{π}{2}} : \frac{14}{π} [sin (u)]_{0}^{\frac{π}{2}}

= \frac{14}{π} [sin (u)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= \frac{14}{π} \cdot 1

Simplify

= \frac{14}{π}

\int_{- 1}^{1} (1 + x) 1 - x^{2} d x

\int_{0}^{4} x x^{2} + 10 d x

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\int_{1}^{2} x^{2} + x d x

\int_{0}^{\frac{π}{4}} sin^{7} (2 x) d x

What is the integral from 0 to 1 of 7cos((pit)/2) ?
The integral from 0 to 1 of 7cos((pit)/2) is (14)/pi