Consider the integral- 5int9 4x4 dx find the riemann sum

Question

1. Consider the integral

₅∫⁹ ((4/x)+4) dx

a) Find the Riemann sum for this integral using right endpoints and n = 4.

b) Find the Riemann sum for this same integral, using left endpoints and n  4.

2. Use the Midpoints Rule to approximate

_-1.5∫^5.5 x³dx

With n = 7.

3. Consider the graph of the function f(x):

Evaluate the following integrals by interpreting them in terms of areas:

a) ₀∫² f(x) dx =

b) ₀∫⁵ f(x) dx =

c) ₅∫⁷ f(x) dx =

d) ₀∫⁹ f(x) dx =  

4. Consider the graph of the function g(x):

The graph from x = 2 to x = 6 is a semicircle. Evaluate the following integrals by interpreting them in terms of areas:

a) ₀∫² g(x) dx =

b) ₂∫⁶ g(x) dx =

c) ₀∫⁷ g(x) dx =

5. Find a and b.

₇∫²⁰ f(x) - ₇∫¹⁴ f(x) = _a∫^b f(x)  

6. Let ₁∫^5.5 f(x)dx = 8, ₁∫^2.5 f(x)dx = 10, ₄∫^5.5 f(x)dx = 5.

Find _2.5∫⁴ f(x)dx =

And ₄∫^2.5 (8f(x) - 10)dx =

7. Given that 1 ≤ √(x³ + 1) ≤ on [0, 2] to estimate ₀∫² √(x³ + 1)dx.