(Hint: Complete the square under the radical.) Find the area of the region bound

Question

(Hint: Complete the square under the radical.) Find the area of the region bounded by x = 0, x = 2, and y = 0. Find the area of the region bounded by x = 0, x = 2, and y = 0. Find the area of the region bounded by y = ln 2x, x = 1 / 2, x = 1, and y = 0. Find the area of the region bounded by y = x2ex, x = 0, x = 2, and y = 0. Find the volume of the solid generated by revolving the region bounded by y = ex, y = 0, x = 0, and x = 1 about the y-axis. Find the volume of the solid generated by revolving the region bounded by y = sin x, y = 0, x = 0, and x = pi about the y-axis.

Explanation / Answer

2). Use integral by part n put u=x n v= cos(x) 4). Same as 2 put u=x and v = e^-x 6).Put ln(x)=t and then use by parts and solve 8).Same as 6 9). Put x=cos(t) and then dx = -sin(t) dt and use trigo formulas to solve 22).Put x=Sin(t) and then same as 9. 23). put x=(t^2 + 1) and solve, it will e easy 2). Put 4x=3Sin(t) and solve it will be easy 3). Put 3x = 2sin(t) and solve 7). Put x= 2Sin(t) and solve 11). Put x = 3Sec(t) and solve it will be easy 19). Put x=3Sec(t) and solve it will be easy 20). Put x=Sin(t) and solve it will be easy

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