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Suppose that f is a continuous function that satisfies
"f(x)=x\\int_{0}^{x} f(t)dt + x\u00b3"
For all x and that f(a) = 1, a ∈ R. Express f ' (a) in terms of a only:
The area under one arch of the sine curve revolves about the x-axis. Find the volume generated.
Find the surface area generated by revolving about x-axis the area in the second quadrant under the curve y=ex.
Find the area bounded bounded by the following curves, y=x2/4 and x+4=2y.
Find the centroid of the area bounded by the parabola y=x2 and the line 2x+3.
Find the moment of inertia of the area of the loop y2=x2(1-x), with respect to y-axis
Find the area of the surface that is generated by revolving the portion of
the curve y = x
3 between x = 0 and x = 1 about the x −axis.
Integrate ln(2x+2) from -1<=x<=1
a) find and classify the critical points of the functions f(x) = 2x^3 + 3x^2 - 12 x +1 into maximum, minimum and inflection points as appreciate.
(b) The sum of two positive numbers is S. find the maximum value of their product.
#340153 on Dec 2023