Short Question 2 – 4


Question 2:
Given that  Given that4(1+x)4dx=m(1+x)n+c,
find the values of m and n.

Solution:
4(1+x)4dx=m(1+x)n+c4(1+x)4dx=m(1+x)n+c4(1+x)33(1)+c=m(1+x)n+c43(1+x)3+c=m(1+x)n+cm=43,n=3



Question 3:
Given 212g(x)dx=4, and 21[mx+3g(x)]dx=15.Find the value of constant m.

Solution:
21[mx+3g(x)]dx=1521mxdx+213g(x)dx=15[mx22]21+321g(x)dx=15[m(2)22m(1)22]+32212g(x)dx=152m12m+32(4)=15given212g(x)dx=432m+6=1532m=9m=9×23m=6



Question 4:
Givenddx(2x3x)=g(x), find21g(x)dx.

Solution:
Givenddx(2x3x)=g(x)g(x)dx=2x3xThus,21g(x)dx=[2x3x]21=2(2)322(1)31=41=3