1 / | | / ___ \ | \sin(pi*x) - \/ x + 1/ dx | / -1
Integral(sin(pi*x) - sqrt(x) + 1, (x, -1, 1))
Integrate term-by-term:
Integrate term-by-term:
The integral of a constant times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
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 sine is negative cosine:
So, the result is:
Now substitute back in:
The result is:
The integral of a constant is the constant times the variable of integration:
The result is:
Add the constant of integration:
The answer is:
/ | 3/2 | / ___ \ 2*x cos(pi*x) | \sin(pi*x) - \/ x + 1/ dx = C + x - ------ - --------- | 3 pi /
4 2*I - - --- 3 3
=
4 2*I - - --- 3 3
4/3 - 2*i/3
(1.33413269908838 - 0.665867300911624j)
(1.33413269908838 - 0.665867300911624j)
Use the examples entering the upper and lower limits of integration.