Math 19B Miligore Midterm Review - Calculus 19B Review Exam...

Calculus 19B Review Exam 1
Migliore
1. Approximate the area under a curve using equal subintervals with left endpoints, right
endpoints or midpoints.
2. Rewrite a definite integral as the limit of a Riemann sum.
3. Rewrite the limit of a Riemann sum as a definite integral.
4. Evaluate a definite integral by interpreting the integral as the area of a geometric
object whose area formula is known, e.g. circle or triangle.
5. Find a 1  such that
 
a
0
x 3 dx 0.  

6. Given that:
10
1
f(x)dx 5 

,
10
5
f(x)dx 2 

, and
1
g(x)dx 8. 

|
Find
 
1
3f(x) 4g(x) dx 

.
7. Find the derivatives of functions defined as definite integrals, e.g.
2
ln x
2
d
e dt
dx

.
8. Evaluate definite integrals by using the fundamental Theorem of Calculus,
b
a
f(x)dx F(b) F(a)  

, where
3
5
5
t