Question

Evaluate :
i. ${\int }_0^{\pi /2}(\sin x+\cos x)dx$
ii. ${\int }_0^1(3x^2+4)dx$
iii. ${\int }_0^1(3e^{3x}+e^{-x})dx$

• A. i. 2
  ii. 5
  iii.$\frac{e^4-1}{e}$
• B. i. 3
  ii. 4
  iii.$\frac{e^3-1}{e}$
• C. i. 9
  ii. 5
  iii.$\frac{e^3-1}{2e}$
• D. i. 1
  ii. 4
  iii.$\frac{e^3-1}{3e}$

Answer 1

The correct option is A i. 2

ii. 5
iii.$\frac{e^4-1}{e}$
a. ${\int }_0^{\pi /2}(\sin x+\cos x)dx$
$=[-\cos x{]}^{\pi /2}0+[\sin x{]}_0^{\pi /2}=(-0+1)+(1-0)=2$
b. ${\int }_0^1(3x^2+4)dx=[x^3{]}_0^1+4[x{]}_0^1=1+4=5$
c. ${\int }_0^1(3e^{3x}+e^{-x}dx=[e^{3x}{]}_0^1+[-e^{-x}{]}_0^1$
$e^3-1)+(-\frac{1}{e}+1)=\frac{e^4-1}{e}$