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The volume of the solid of revolution formed when the area between y and y is rotated about the y- axis, is… A. xdx B. 2πyydy C. πxdx D. πyydy
Find the area of triangle determinied by the point P(-3,1-1) Q(-2,0,5) and R(-4,-1,2).
f(x,y)=−2x^2+4y^2
find the value of the directional derivative at the point (3,4) in the direction given by the angle θ=2π/5. More specifically, find the directional derivative of f at the point (3,4) in the direction of the unit vector determined by the angle θ in polar coordinates.
Evaluate the integral using a rational function ∫▒(cos x)/(√sin+ ∛(sin⁡x )) dx
(a) Create a function that is a product of two non-constant functions that would NOT require the product rule to differentiate it.

(b) Differentiate your function from part (a) without using the product rule.

(c) Differentiate your function from part (a) by using the product rule and confirm your result is equivalent to your result in part (b) by simplifying.
(a) Create a function that is a product of two non-constant functions that would NOT require the product rule to differentiate it.

(b) Differentiate your function from part (a) without using the product rule.

(c) Differentiate your function from part (a) by using the product rule and confirm your result is equivalent to your result in part (b) by simplifying.

Evaluate the integral ∫x^3 sin⁡〖x〗dx


Evaluate the integral ∫▒(〖cos〗^5 (lnx) 〖sin〗^2 (lnx))/x dx
Evaluate the integral ∫▒(〖tan〗^4 x+〖tan〗^6 x)/(〖tan〗^4 x-1) dx
Evaluate the integral ∫_(-1)^1▒1/√(x^2+2x+2) dx
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