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help? area? curves?

0 votes

asked May 15, 2015 in CALCULUS by anonymous

2 Answers

0 votes

1)

Step 1:

The curve is .

Graph the curve  .

Determine the area below the curve and above the axis.

Observe the graph:

The region shaded in blue colour is the required area of the region.

The points of intersection are and .

Step 2:

Definite integral as area of the region:

If image and image are continuous and non-negative on the closed interval image,then the area of the region bounded by the graphs of image and image and the vertical lines image and image is given by

image.

Here image and image.

Integral limits are and .

Apply power rule of integration: image.

Area of the required region is .

Solution:

Area of the required region is .

answered May 15, 2015 by cameron Mentor
0 votes

2)

Step 1:

The curve is .

Graph the curve  .

Determine the area right of the curve and left of the axis.

Observe the graph:

The region shaded in pink colour is the required area of the region.

The points of intersection are and .

Step 2:

Definite integral as area of the region:

If image and image are continuous and non-negative on the closed interval image,then the area of the region bounded by the graphs of image and image and the lines and is given by

, .

Here image and .

Integral limits are and .

image

image

image

Apply power rule of integration: image.

image

image

image

image.

Area of the required region is image.

Solution:

Area of the required region is image.

answered May 15, 2015 by cameron Mentor

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