1 / | | / 2\ | sin\x + y / | ----------- dx | 2 | / 0
Integral(sin(x + y^2)/2, (x, 0, 1))
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of sine is negative cosine:
Now substitute back in:
So, the result is:
Add the constant of integration:
The answer is:
/ | | / 2\ / 2\ | sin\x + y / cos\x + y / | ----------- dx = C - ----------- | 2 2 | /
/ 2\ / 2\ cos\y / cos\1 + y / ------- - ----------- 2 2
=
/ 2\ / 2\ cos\y / cos\1 + y / ------- - ----------- 2 2
cos(y^2)/2 - cos(1 + y^2)/2
Use the examples entering the upper and lower limits of integration.