Use Wolframalpha to find the exact volume of the solid obtained by rotating about x = [pi]/2 the region bounded by y = sin^2x, y = sin^4x, x in [0,[pi]/2]. [Notation: c in [a, b] means a leq c leq b.]

Step-by-step explanation:

Here the region between two curves is rotated about a vertical line.

The functions are

Intersecting points are x=0 and x =pi/2

Since rotated about x = pi/2 we get

using cylindrical shell method

Volume =

From wolfram alpha we find that

Volume=

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step-by-step explanation:

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1