Week 8 - Integration

Question 1

a) Integrate x^2*sin(3x). Is our answer of the correct form?

b) Integrate x^2*sin(3x)  between 0 and 2π.

c) Now make a plot of x^2*sin(3x)  between 0 and 2π. Use the graph to explain why by observation you can predict that your solution to part ‘b’ will be negative. (hint: consider the magnitude of the adjacent peaks and troughs).

Question 2

a) Create a function f(a,b)= (∫_a^b)sin(x)*(x-π)^2dx.

b) Evaluate the function with a=0,b=π.

c) Now evaluate the function with a=0,b=2π.

d) Plot sin(x)*(x-π)^2 from 0 to 2π.

e) Explain your solutions to part ‘b’ and part ‘c’ with reference to you plot from part ‘d’