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help?[substitution definite integral]??

0 votes

asked May 14, 2015 in CALCULUS by anonymous

4 Answers

0 votes

(1)

Step 1:

 The integral is image.

Let image.

Apply derivative on each sid with respect to image.

image

image

image

image.

Step 2:

Substitute image and image in integral.

image

image

image

image

image

image

Substitute image.

image

image

image

image

image

image

image

image.

image.

Solution:

image.

answered May 14, 2015 by Sammi Mentor
0 votes

(2)

Step 1:

The integral is .

Let

Apply derivative on each side with respect to .

.

Substitute and in the integral.

Again using substitution method.

Let image.

Apply derivative on each side with respect to image.

image

image

image.

Step 2:

Substitute image and image in image.

image

image

image

image

image

image

image

answered May 14, 2015 by Sammi Mentor
edited May 14, 2015 by Sammi

Contd...

Substitute image.

image

Substitute .

image

image

image

image

image

image

image

image.

image.

Solution:

image.

0 votes

(3)

Step 1:

The integral is .

Sum property of Integral :.

Find the value of image.

image

image

image.

Step 2:

Find the value of .

Apply derivative on each side with respect to image.

Substitute  and  in .

Integration of exponential function :.

image.

answered May 14, 2015 by david Expert
edited May 14, 2015 by david

Contd..

Step 3:

imageimage

image

image

image

image

image.

Solution:

image.

0 votes

4)

Step 1:

The integral is .

 

Evaluation of the integral is not possible.

image

Continuity Implies Integrability Theorem:

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

The function image is not continuous at image on image.

The second term in the integral image cannot be integrated on image.


If even one term in the integral cannot be integrated then the whole integral cannot be done.

Solution:

Evaluation of the integral is not possible.

answered May 14, 2015 by david Expert
edited May 14, 2015 by david

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