How do you evaluate the definite integral $\int sin (4 x)$ $int sin(4x)$ from $[0, \frac{π}{8}]$ $[0,pi/8]$ ?

Question

How do you evaluate the definite integral $\int sin (4 x)$ $int sin(4x)$ from $[0, \frac{π}{8}]$ $[0,pi/8]$ ?

1 Answer

Impact of this question

3254 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-04T03:04:44

$\frac{1}{4}$ $1/4$

Explanation:

This is a fairly common integral.

$\int sin (a x) d x = - \frac{1}{a} cos (a x)$ $intsin(ax)dx=-1/acos(ax)$ where $a$ $a$ is any constant.

So,

$\int_{0}^{\frac{π}{8}} sin (4 x) d x = - \frac{1}{4} cos 4 x {∣ ∣ ∣}_{0}^{\frac{π}{8}}$ $int_0^(pi/8)sin(4x)dx=-1/4cos4x|_0^(pi/8)$

Evaluating, we get

$- \frac{1}{4} cos (\frac{4 π}{8}) - (- \frac{1}{4} cos (0)) = - \frac{1}{4} cos (\frac{π}{2}) + \frac{1}{4} cos (0) = \frac{1}{4}$ $-1/4cos((4pi)/8)-(-1/4cos(0))=-1/4cos(pi/2)+1/4cos(0)=1/4$

As $cos 0 = 1$ $cos0=1$

Science

Math

Humanities

... and beyond

How do you evaluate the definite integral $\int sin (4 x)$ $int sin(4x)$ from $[0, \frac{π}{8}]$ $[0,pi/8]$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you evaluate the definite integral int sin(4x)∫sin(4x)int sin(4x) from [0,pi/8][0,π8][0,pi/8]?

1 Answer

Explanation:

Related questions

Impact of this question

How do you evaluate the definite integral $\int sin (4 x)$ $int sin(4x)$ from $[0, \frac{π}{8}]$ $[0,pi/8]$ ?