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Finding Integrals (8 Problems)

(See attached file for full problem description with proper symbols)

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Answers and working for Integration questions:

1.Integrate the following functions with respect to .

(i) sin(5 - 4)
(ii) cos(3 - 2)

2. Integrate the following functions with respect to x.

(i) 4e-3x
(ii) (3 + 4x)-1
(iii) -6 .
2 - 5x
(iv) 5 - 3e4x
ex

3. Evaluate the following definite integrals.
/3
(i)  cos(2)d
0

0. 5
(ii)  sin(1.6 + 3)d
0.1

1
4. Evaluate  (3 - e4x)dx
0

4
5. Evaluate  1 dx
3 1 + 4x

0
6. Evaluate  5 dx
-1 3 - 2x

-2
7. Evaluate  e3x - 4 dx
-3 ex

8. The mean value of a continuous function over a given range is defined as the integral of the function divided by the range.
b
Mean value of (x) from a to b = 1  (x)dx
b - a a

Determine the mean value of the function 1 - e-t/T from t = 0 to t = T.

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Integrals are found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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