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help [[integrals]]??

0 votes

asked May 15, 2015 in CALCULUS by anonymous

3 Answers

0 votes

(10)

Step 1:

The integral is .

Continuity Implies Integrability Theorem:

If a function is continuous on the closed interval , then is integrable on .

exists.

Consider the function .

The function is continuous on the interval .

is exists.

Step 2:

Evaluation of integral:.

.

.

Solution:

.

answered May 15, 2015 by Sammi Mentor
0 votes

(9)

Step 1:

The integral is .

Continuity Implies Integrability Theorem:

If a function is continuous on the closed interval , then is integrable on .

exists.

Consider .

The function is a linear function.

The function is continuous at every real number.

The function is continuous on the interval .

is exists.

Step 2:

Evaluation of integral:.

Apply sum and difference rule in integration: .

.

.

Solution:

.

answered May 15, 2015 by Sammi Mentor
0 votes

(11)

Step 1:

The integral is .

Continuity Implies Integrability Theorem:

If a function is continuous on the closed interval , then is integrable on .

exists.

Consider the function .

Graph the function: .

image

Observe the graph:

The function is continuous on the interval .

is exists.

answered May 15, 2015 by Sammi Mentor

Contd...

Step 2:

Evaluation of integral:.

Apply special integration formula: image.

In this case and .

image

.

.

Solution:

.

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