What is the integral from 0 to 1 of (3x+1)cos(x) ?

The integral from 0 to 1 of (3x+1)cos(x) is 4sin(1)+3cos(1)-3

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integral from 0 to 1 of (3x+1)cos(x)

\int_{0}^{1} (3 x + 1) cos (x) d x

4 sin (1) + 3 cos (1) - 3

Decimal Notation

1.98679 \dots

Solution steps

\int_{0}^{1} (3 x + 1) cos (x) d x

Apply Integration By Parts

: [(3 x + 1) sin (x) - \int 3 sin (x) d x]_{0}^{1}

= [(3 x + 1) sin (x) - \int 3 sin (x) d x]_{0}^{1}

\int 3 sin (x) d x = - 3 cos (x)

= [(3 x + 1) sin (x) - (- 3 cos (x))]_{0}^{1}

Simplify

= [sin (x) (3 x + 1) + 3 cos (x)]_{0}^{1}

Compute the boundaries:

4 sin (1) + 3 cos (1) - 3

= 4 sin (1) + 3 cos (1) - 3

\frac{d}{d x} (- 9 x^{2} + 4 x + 5)

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\frac{d y}{d x} = \frac{y}{x}

\int \frac{1}{( π x - 1 )} d x

\int 4^{l n (x)} d x

What is the integral from 0 to 1 of (3x+1)cos(x) ?
The integral from 0 to 1 of (3x+1)cos(x) is 4sin(1)+3cos(1)-3