Calculus Answers

Given that d/dx(xlnx−x)=lnx, find the volume of the solid obtained by rotating, about the x-axis, the graph of the function y=√(lnx) from the x-intercept and x=e^2.

Find the area bounded by y=cosx, the x-axis and between x=−π/2 to x=π/2. Draw a sketch for yourself to help you find the integral.

Find the volume of the solid with cross-sectional area 2/√(1−4x^2) lying between x=0 and x=12

Find the area of the region enclosed between the graphs of y=ex and y=e−x and the line x=ln2.

Evaluate the following limit:
limt→1−t2−|t−1|−1|t−1|.

Integrate the following functions wrt x
I) 1/(2x+1)^3/2
ii) sin(2x+3)
iii)cosec(4x)
iv)1/√(1-9x^2)
v)1/(1+4x)

Consider the parametric curve described by r(t) =〈2 sin(3t), √4t, 2cos(3t)〉. Find the unit tangent vector of r(t).

Consider the parametric curve described by r(t) =〈2 sin(3t), √4t, 2cos(3t)〉. Find the unit tangent vector of r(t).

Consider the parametric curve described by r(t) =〈2 sin(3t), √4t, 2cos(3t)〉. Find the unit tangent vector of r(t).

Consider the parametric curve described by r(t) =〈2 sin(3t), √4t, 2cos(3t)〉. Find the unit tangent vector of r(t).