MAT 103 Assignment Problem 5.4

MAT 103 Assignment Problem 5.4 | Borough of Manhattan Community College

5.4 The Fundamental Theorem Of Calculus

Question 1

1 point) Evaluate the definite integral:

Question 2

(1 point) Evaluate the definite integral:

Question 3

(1 point) Evaluate the definite integral.

Question 4

(1 point) Evaluate the definite integral

∫π010sin(x)dx

Question 5

(1 point) Evaluate the integral

∫34sin(t)dt

Question 6

(1 point) Evaluate the definite integral

Question 7

1 point) Evaluate the integral ∫10x5/6dx.

Question 8

(1 point) Evaluate the integral ∫π/40secθtanθdθ.

Question 9

1 point) Evaluate the integral ∫40(2ex+6cosx)dx.

Question 10

(1 point) Evaluate the definite integral

∫645x√dx∫465xdx

Question 11

1 point) Evaluate the definite integral

∫2−2(4−x2)dx

Question 12

(1 point) Evaluate the definite integral

∫626x2+8x√dx

Question 13

(1 point) Evaluate the definite integral.

Question 14

(1 point) Evaluate ∫π−πf(x)dx∫−ππf(x)dx, where

f(x)={2x4,7sin(x),−π≤x<00≤x≤π.f(x)={2x4,−π≤x<07sin⁡(x),0≤x≤π.

Question 15

(1 point) Find the area of the region bounded by the graphs of the equations

y=7x2+2y=7x2+2, y=0y=0, x=1x=1, x=6

Question 16

(1 point) Use the Second Fundamental Theorem of Calculus to find the derivative of the following function.

g(r)=∫r0x2+16−−−−−−√dx

Question 17

(1 point)

Let g(x)=∫x5−8t2dt.g(x)=∫5x−8t2dt. Find g′(x).

Question 18

(1 point)

Let g(x)=∫x1−9ln(t)dt.g(x)=∫1x−9ln⁡(t)dt. Use the Second Fundamental Theorem of Calculus to find g′(x).

Question 19

1 point) Let f(x)=∫x3t4dtf(x)=∫3xt4dt. Evaluate the following.

Question 20

(1 point)
G(x)=∫x1tantdt

Question 21

Question 22

(1 point)
Below is the velocity function, in feet per second, for a particle moving along a straight line.
Find (a) the displacement and (b) the total distance that the particle travels over the given interval.

v(t)=t3−13t2+44t−32v(t)=t3−13t2+44t−32 1≤t≤5

Question 23

(1 point) Use the Fundamental Theorem of Calculus to decide if the definite integral exists and either evaluate the integral or enter DNE if it does not exist. If the value does exist, you need to simplify the answer completely.