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

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Answer 1 · 2016-09-20T11:31:19

#0#.

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

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

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

#" then, "int_-a^a f(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]_-1^1#

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

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