How do you evaluate the definite integral int 5x^3 dx5x3dx from [-1,1][1,1]?

1 Answer
Sep 20, 2016

00.

Explanation:

Using the following well-known Result , we can immediately say,

without any calculation , that, int_-1^1 5x^3dx=0115x3dx=0.

" Result : If f is continuous odd function defined on "[-a,a], Result : If f is continuous odd function defined on [a,a],

" then, "int_-a^a f(x)dx=0 then, aaf(x)dx=0.

However, we work out the Soln. as shown below :-

I=int_-1^1 5x^3dx=5int_-1^1 x^3dx=5[x^4/4]_-1^1I=115x3dx=511x3dx=5[x44]11

=5/4[1-(-1)^4]=5/4[1-1]=54[1(1)4]=54[11].

:. int_-1^1 5x^3dx=0.