A function is defined by

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

A function

f

is defined by

f(x)=3 x^{n}

, where

n

is a real number different from

-1

. Let

F(x)

be an antiderivative of

f

such that the curve

y=F(x)

passes through the points

(1,5)

and

(3,31)

. (i) Write

F(x)

in terms of

n

and the constant of integration

C

. (ii) Form equations by substituting the given points and hence find the exact values of

n

and

C