Question

The base of a solid is the region between the curve yequals3 cosine x and the ​x-axis from xequals0 to x equals StartFraction pi Over 2 EndFraction . The cross sections perpendicular to the ​x-axis are squares with bases running from the ​x-axis to the curve. Find a formula for the area​ A(x) of the cross sections of the solid perpendicular to the​ x-axis.

Answer 1

Answer:

A=3(π/2)-1 au

Step-by-step explanation:

we have according to the graph that

f(x)=3

g(x)=cos(x)

Knowing A=∫|f(x)-g(x)|dx, then

$A=\int\limits^a_b (f(x)-g(x)}) \, dx$; where a=0 and b=π/2

$A=\int\limits^a_b (3-cos(x)){} \, dx$

A=(3x-sin(x)) evaluated  0 ≤ x ≤ π/2

A=(3(π/2)-sin(π/2))-(3.0-sin(0))

$A=3\frac{\pi }{2}-1$