Question$-2)$ Please calculate the following integrals.

a$){\displaystyle \underset{0}{\overset{1}{}}}\frac{x^3}{x^2+2x+1}dx$

b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2x-4}{(x^2+1)(x-1{)}^2}dx$

c$){\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{ln}}{}}}2x{e}^{x^2}sin(e^{x^2})dx$

d$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(6x^2-4x+3)dx$

Question$-3)$ A ball is dropped from a height of $20$ meters. Each time it hits the ground, it bounces to

$70$ percent of the previous height. Please answer the following questions based on given:

a$)$ Write general expression for the distance travelled by ball $?$

b$)$ Determine whether this series converges or diverges? Why?

c$)$ If the series converges, find the total distance traveled by the ball.

Question$-4)$ Find the area of the region enclosed by the following curves ; $y=x^2,y=x+6,x=0,$ and

$x=5.$ Show your all work.

NOTE: To draw the graph of given function, you can use Matlab, Desmos $2$D $($recommended$),$ or the$$

x

$3$

x

$2+2$x $+1$

$1$

$0$

dx