Let R denote the region bounded by the curve y=x^3 and the lines x=0 and x=4. Find the volume generated when R is rotated 360 degrees about the x axis.
The area of a circle is given by (pi)r2 and the area generated by R can be considered as an infinite number of circular areas.
Thus, we can write the area generated by R as the integral of (pi)(x3)2 between x=0 and x=4.
The (indefinate) integral is: (pi)6x5
so the area is: (pi)6(45-05)=(pi)6(1024-0)
=6144(pi)
SB
Related Maths A Level answers
All answers ▸Solve the following equation, give the answer/answers as coordinates. y=3x^2 , y=2x+5.
Solve the equation sec^2(A) = 3 - tan(A), for 0<= A <= 360 (degrees)
The curve C has a equation y=(2x-3)^5; point P (0.5,-32)lies on that curve. Work out the equation to the tangent to C at point P in the form of y=mx+c
The polynomial p(x) is given by p(x) = x^3 – 5x^2 – 8x + 48 (a) (i) Use the Factor Theorem to show that x + 3 is a factor of p(x). [2 marks] (ii) Express p(x) as a product of three linear factors. [3 marks]