Short Question 14 & 15


Question 14 (3 marks):
It is given that 5(2x+3)ndx=p(2x+3)5+c , where c, n and p are constants.
Find the value of n and of p.

Solution:
5(2x+3)ndx=5(2x+3)ndx=5(2x+3)n+1(n+1)×2+c=52(1n)×1(2x+3)n1+c=52(1n)(2x+3)n1+cCompare 52(1n)(2x+3)n1with p(2x+3)5n1=5n=652(1n)=p52(16)=p52(5)=pp=12



Question 15 (4 marks):
Diagram shows the curve y = g(x). The straight line is a tangent to the curve.
Diagram

Given g’(x) = –4x + 8, find the equation of the curve.


Solution:
Given g'