Find the volume of the solid with cross-sectional area extending over the range .

Question

Find the volume of the solid with cross-sectional area  extending over the range  .

Quizplus · Accepted Answer

Since the solid has a cross-sectional area of 11eaa88b_9186_9c54_a696_1554b74472f1_TB5869_11 and extends over the range 11eaa88b_9186_c365_a696_0bc8c1c4a57f_TB5869_11, we can use the formula:

Volume = ∫A(x)dx

where A(x) is the area of the cross-section at a given value of x.

Since the cross-section is constant, we have:

A(x) = 11eaa88b_9186_9c54_a696_1554b74472f1_TB5869_11

and

∫A(x)dx = A(x)∫dx = A(x)x + C

where C is the constant of integration.

Evaluating this expression over the range 11eaa88b_9186_c365_a696_0bc8c1c4a57f_TB5869_11 gives:

Volume = A(x)x ∣ 11eaa88b_9186_c365_a696_0bc8c1c4a57f_TB5869_11 = (11eaa88b_9186_9c54_a696_1554b74472f1_TB5869_11) (11eaa88b_9186_c365_a696_0bc8c1c4a57f_TB5869_11)

Simplifying, we get:

Volume = 11eaa88b_9186_c366_a696_adb0d6471544_TB5869_11

Therefore, the answer is (A).

Find the Volume of the Solid with Cross-Sectional Area