The goal is to approximate and then compute exactly the

Question

Question 01: The curve in red in the pictures below is the graph of y = x2 + 1.

The goal is to approximate and then compute exactly the area between the x-axis and the graph of y = x2 + 1 with x between 0 and 2. (Use Left Hand Riemann Sum with 4 sub-intervals)

Question 02: Find the derivative of

 

Question 03: Evaluate the Integral: ∫x² 1n (x) d_x

Question 04: In each case use substitution to find the integral:

 

Question 05: Evaluate integration of: 

Question 06: Use Trapezoidal rule to approximate the area under sin(x) from x=0 to x=pi/2 using 3 sub-intervals.

Question 07: Solve the differential equations: