Answer to Question #31049 in Integral Calculus for Aaron Okievs.

Question

Integrate with respect to x: ∫ x^6 dx

a. x^7/7+c

b. x^6/7+c

c. x^5/5+c

d. x^2/2+c

Answer 1

∫ x^6 dx
We know that for every n( n is not equal to 0) ∫ x^ndx=x^(n+1)/(n+1) + const
In our case n=6, therefore ∫ x^6 dx=x^(6+1)/(6+1) +const=x^7/7 +c

Thus, the right answer is a. x^7/7+c