answer only 3, 4 and 5 please Show that using the substitution x = 2 tan theta F

Question

answer only 3, 4 and 5 please

Show that using the substitution x = 2 tan theta Find the area enclosed by the curves y1 (x) = 5x - x2 and y2 (x) = x. Now find the volume when the region above is rotated around the x- axis. Find the volume of the solid whose base is the circle of radius 2 centered at (0,0) in the x-y plane and whose cross section perpendicular to the x-axis is a right triangle with hypotenuse in the x-y plane. Recall the exponential density function is f(x) = { It the mean for this distribution is 4, find P(4

Explanation / Answer

4. The equation of circle is x^2 + y^2 = 4 as its centre is (0,0) and radius 2.

    Since, the hypotenuse lies on the x-y plane, So, the volume is

    V = 2*(integration of (4-x^2) dx) under the limits 0 to 2.

    So, the answer is 10.67 units^3.

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