We partially grate a carrot. We represent the root as a cylinder: x ^ 2 + y ^ 2 = 1 from z = 0 to a height of 15cm. We represent the rasp as the plane: x + y + z = 6. Calculate the volume...

We partially grate a carrot. We represent the root as a cylinder: x ^ 2 + y ^ 2 = 1 from z = 0 to a height of 15cm. We represent the rasp as the plane: x + y + z = 6. Calculate the volume...

Sin-1logx find integral

a. Explain why ∫02pi sin(x)dx = 0 b. Can you set up another integral, or perhaps multiple integrals, to compute the total (unsigned) area between sin(x) and the x-axis on...

Find the area bounded by the curve: y = x(x-1)^2, the line y = 2, and the y - axis

Set up an iterated integral to evaluate I=R⌠⌠⌠f(x,y,z) dv, where R is the region in the first octant bounded by the surface z=x+y^2, the cylinders y=2sqrt(x), x=2sqrt(y), and the xy-plane The...

What is the volume of the region bounded by y^2 + 2y + 4x - 3 =0 and x^2 - 2x - 4y - 3 = 0, and the axis of revolution is at a.) Y= -1 b.) X=3 c.) X=4

Evaluate S⌠⌠(∇xF)•ndS where S is the portion of the ellipsoid x^2+y^2+4z^2=4 below the xy-plane, n points to the convex side of S, and F(x,y,z)= <exp{z^2}, z-y, 3xsiny>...

If the substitution √(X)=sin y is made in the integrand of: (top of the integral sign is (1/2), bottom of the sign is 0) ∫ ( √(X) )/( √(1-X) )dx, the resulting integral is_____________. A...

Evaluate the integral (1/sqrt(x^2 - 5))dx on limits of 3 to 4, using the formula: integral of (1/sqrt(x^2 - a^2))dx. Recall that this formula was found by using the substitution x = a cosh t,...

Find an anti-derivative F(x) with F'(x) = f(x) and F(0)=0 f(x)=(1/5)x

∫(x+5)/(√9-(x-3)2) This problem is stumping me! Also the square root is over the whole denominator.

∫1/(√x√(1-x)) dx

The curve is x^3-6x^2+11x-6. I have to prove that the two regions enclosed between the x-axis and the curve are equal. Given is, that the curve cuts the x-axis at x=1,x=2 and x=3. I tried finding...

What is a particular solution of the indefinite integral ∫(2)/(1-x2)dx that passes through (√3 , (Π/2)? a) f(x)=√(3) tan-1x-(Π/6) b) f(x)=2tan-1x-(Π/6) c) f(x)=2tan-1x+...

∫ ( (dx)/√(x2+36) )=_____________ a. ( (√(x2+36)+x)/6 )+C b. ln abs( (x+6)/(√(x2+36)) )+C c. ln ( (√(x2+36)+x)/6...

what integral formula would represent the area between the curves f(x)=-x2+2x+3 and g(x)=x+1 on the interval [-1,2]?

Find the integral below. ∫∫1_R^ (x+2y) dar={(x, y):0≤x≤3, 1≤y≤4}

Evaluate the integral below given R. (Hint: what is the upper boundary of x?) ∫∫1_R^ xy da R bounded by x=0 y=0y=9−x^2 ...

What is the area of the region bounded by the curves y=2(x^2)-7 and y=2/x between x=1 and x=3? Please and thank you!

The Chain Rule for antiderivatives is also known as the ___________________ rule. -derivative -substitution -product -integral