The University of Texas Area Distance and Definite Integral Questions Questions are about Area distance, definite integral and fundamental theorem of calcu

The University of Texas Area Distance and Definite Integral Questions Questions are about Area distance, definite integral and fundamental theorem of calculus. I want complete works on each question. The questions are in attachments. Remember to show work!
Remember to check your answers!
Problems continue on the next page.
1
x + 3.
X =
1. Let f(x)
za
(a) (3 points) Sketch the region S below the graph of y = f(x) and between x = 0 and
4. Remember to label axes and important points!
(b) (4 points) Approximate the area A of the region S using rectangles by dividing
[0, 4) into four equal subintervals and creating rectangles with the right endpoints.
Here you will be calculating R4. It may help to draw the rectangles on your graph.
(c) (2 points) Now use geometry to determine the exact area A of the region S.
(d) (1 point) Was your approximation an overestimate or an underestimate of the ac-
tual area?
2. (3 points) Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of
the following function:
Cr4
g(x) =
sin ? cos ?d?
3. Use Part 2 of the Fundamental Theorem of Calculus to evaluate the following definite
integrals. Make sure you include all steps – antiderivative, evaluating the antiderivative,
final answer.
4.05/2 dx
(a) (4 points) [(4 – 23)d:
(b) (4 points) [° 4
(©) (4 points) [
le
(a) (4 points) |
(ex – x4)dx
sec 0 tan Odo

Purchase answer to see full
attachment