MAT 103 Assignment Problem 5.1

MAT 103 Assignment Problem 5.1 | Borough of Manhattan Community College

5.1 Antiderivatives and Indefinite Integrals

Question 1 Consider the function f(x)=9x9+4x5−7x3−4f(x)=9x9+4x5−7x3−4.
Enter one of the antiderivatives of f(x)f(x) (You can choose C to be any number) 

 

Question 2

(1 point) Find the most general antiderivative for the function 5u4−4u3−45u4−4u3−4.
Note: Don't enter the +C . It's included for you.

 

Question 3

(1 point) Find the most general antiderivative of the function

 

Question 4

Find the most general antiderivative of f(x)=7x+10x1.7.f(x)=7x+10x1.7.

Note: Any arbitrary constants used must be an upper-case "C".

 

Question 5

Evaluate the following indefinite integral.

 

Question 6

(1 point) Find an antiderivative F(x)F(x) of f(x)=5x−x√f(x)=5x−x.

 

Question 7

(1 point) Find the most general antiderivative of the function

g(x)=x4−−√5+x5−−√4.

Question 8

(1 point) Find the most general antiderivative for the function 16x416x4.
Note: Don't enter the +C . It's included for you.

 

 

Question 9

(1 point) Find the most general antiderivative for the function (3x4−5x3−3)(3x4−5x3−3).
Note: Don't enter the +C . It's included for you.

 

 

Question 10

(1 point) Find the most general antiderivative of the function

f(x)=x(3−x)2.f(x)=x(3−x)2.

 

Question 11

(1 point)
Evaluate the following indefinite integral ∫13sin(x)−4cos(x)dx

 

 

Question 12

1 point)

Find the most general antiderivative of f(t)=8cos(t)−4sin(t).f(t)=8cos⁡(t)−4sin⁡(t).

Note: Any arbitrary constants used must be an upper-case "C". 

 

Question 13

(1 point) Find the most general antiderivative of the function

f(x)=2ex+8sec2x.

 

 

 

Question 14

(1 point) Evaluate the indefinite integral

∫8exdx 

 

Question 15

(1 point) Find the particular antiderivative that satisfies the following conditions:

f′(t)=2et−7;f(0)=7.

 

Question 16

(1 point) Find the particular antiderivative that satisfies the following conditions:

g′(x)=3x2;g(−1)=4.g′(x)=3x2;g(−1)=4.

 

 

 

Question 17

(1 point) Find the particular antiderivative that satisfies the following conditions:

f′′(x)=x2;f′(0)=6f(4)=5.

 

 

Question 18

(1 point) Find the particular antiderivative that satisfies the following conditions:

f′′(x)=sin(x);f′(0)=3f(0)=15.f″(x)=sin(x);f′(0)=3f(0)=15.

 

 

Question 19

(1 point) Evaluate the indefinite integral:

∫6−3xexxdx

 

Question 20

(1 point) Let f(x)=2x−7exf(x)=2x−7ex.
Enter one of the antiderivatives of f(x)f(x) (Constant C can be any number)