Exercises

Take the integral with given limits

1. $x^2-6x+34$ from -3 to 1

   eq1:=x^2-6x+34
int(eq1, x=-3..1)

2. $\sin (x)$ from 0 to Pi

   eq2:=sin(x)
int(eq2, 0..Pi)

3. $\frac{6x^2-15x+12}{x^5+4x^3+4x+3x^4+12x^2+12}$ from 0 to 2

   eq3:=(6x^2-15x+12)/x^5+4x^3+4x+3x^4+12x^2+12
int(eq3, x=0..2)

4. You have taken an internship with a local company that makes businesses handicap accessible. They have discovered that the function
   $\frac{{\left(\sqrt{x}\right)}^3}{12}$
   works well for designing ramps. Your task is to find the surface area of one side of the ramp, i.e. the area under the curve for a ramp of generic length so that an estimate of cost of finishing supplies can be made quickly for a client. Find a function in terms of L, the length of the ramp, that gives the area of one side.

   eq4:=x^(3/2)/12
int(eq4, x=0..L)