1 / | | cos(x) | 4 *sin(x) dx | / 0
Integral(4^cos(x)*sin(x), (x, 0, 1))
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of an exponential function is itself divided by the natural logarithm of the base.
So, the result is:
Now substitute back in:
Add the constant of integration:
The answer is:
/ | cos(x) | cos(x) 4 | 4 *sin(x) dx = C - ------- | log(4) /
cos(1) 2 4 ------ - -------- log(2) 2*log(2)
=
cos(1) 2 4 ------ - -------- log(2) 2*log(2)
2/log(2) - 4^cos(1)/(2*log(2))
Use the examples entering the upper and lower limits of integration.