Question

What does ∫ anx dx = ∫ manx do?

a) ( 1/2a(n-1)xⁿ + C )
b) ( 1/n+1a(n+1)xⁿ+1 + C )
c) ( 1/an⁻1xⁿ-1 + C )
d) ( 1/na(n+1)xⁿ+1 + C )

Answer 1

The integral of anx dx is (1/(n+1))a(x^(n+1)) + C, which corresponds to option b after simplifying the terms.

Step-by-step explanation:

The student's question is concerned with finding the indefinite integral of anx with respect to x. To solve this, we use the power rule for integration, which says that the integral of xn is xn+1/(n+1) plus a constant of integration. Applying this to anx, we multiply the integrating coefficient (a) with the result of the integrated variable.

The correct integral of anx dx is:

( 1/n+1) a (xn+1) + C

This matches option b) ( 1/n+1)a(n+1)xn+1 + C after simplifying the expression, taking into account that a and n+1 are simply factors and can be written as a(n+1).