Exercises

Take the integral with given limits

1. from -3 to 1

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

2. from 0 to Pi

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

3. 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
   
   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)