Question 2:
Given that
Given that∫4(1+x)4dx=m(1+x)n+c,
find the values of m and n.
Solution:
∫4(1+x)4dx=m(1+x)n+c∫4(1+x)−4dx=m(1+x)n+c4(1+x)−3−3(1)+c=m(1+x)n+c−43(1+x)−3+c=m(1+x)n+cm=−43,n=−3
Question 3:
Given ∫2−12g(x)dx=4, and ∫2−1[mx+3g(x)]dx=15.Find the value of constant m.
Solution:
Question 4:
Givenddx(2x3−x)=g(x), find∫21g(x)dx.
Solution:
Givenddx(2x3−x)=g(x)∫g(x)dx=2x3−xThus,∫21g(x)dx=[2x3−x]21=2(2)3−2−2(1)3−1=4−1=3