Finding formulas for the volume enclosed by a hypersphere in n-dimensional space. c) Use a quadruple integral to find the hypervolume enclosed by the hypersphere x^2 + y^2 + z^2 + w^2 = r^2 in R^4. (Use only trigonometric substitution and the reduction formulas for ∫sin^n(x)*dx or ∫cos^n(x)*dx.)
Integrate the function (1/θ)^2 e^((-x1-x2)/ θ)) from 0 to 2 ln 2- x2 (for dx1) and from 0 to 2 ln 2 (for dx2).
Consider a square fan blade with sides of length 2 and the lower left corner placed at the origin. If the density of the blade is ρ(x,y) = 1 + 0.1x, is it more difficult to rotate the blade about the x-axis or the y-axis? Please show steps.
Please see attachment.
Please see attachment.
∫(1 + tanθ)^5sec^2θ dθ
∫ √x sin(1 + x^3/2)dx (Corrected)
∫tan^-1x/(1+x) dx
∫sec2θ tan2θ dθ
∫y^3 √(2y^4 -1)
Please see attachment for integrals substitution.
Can you show me how to integrate ∫ x/(x^2 + 1) dx by substitution?
How do you integrate ∫ x/(x^2 + 1)^2 dx bu substitution?
∫ ( 2 - x) ^ 6 dx
∫ (3x - 2) ^ 20 dx
∫ x^2(x^3+5)^9dx
Which of the following conditions are necessary for a function f to be Riemann integrable on the closed interval [a,b], where a < b? I. f is bounded on [a,b]. II. f is continuous on [a,b]. III. f is differentiable on [a,b].
Please see the attached file for the fully formatted problems. 2. If f(x) =∫ (sin t)^(1/3) dt pi/2 --> x then at what value of x in the interval [0, 2pi] is f(x) a maximum?
Please show all of the steps needed to solve the 6 integrals and differential equations that are attached. A. 3/sqrt(6x - x^2) dx B. 4/(4x^2 + 4x + 65) dx Solve the differential equation. 1. dy/dx = (1 + e^x)^2 2. dr/dt = (1 + e^t)^J/e^t 4. (4 + tn^2x)y' = sec^2 x 5. y' = 1/(x*sqrt(4x^2 - 1))
Please show all of the steps needed to solve the 8 integrals and differential equations that are attached. The integral of x(cos(x) dx The integral of (x^3) sin(x) dx The integral of t(csc(t))cot(t) dt The integral of arctan x dx The integral of e^2x sin(X) dx Solve the differential equation. y' = xe^x2 dy/dt = y
Please give step by step detailed solutions and answers to all. Please oh please do not skip steps. I need to see all these problems done so I can understand them and the way to think of solving them. I cannot find a one on one tutor and since I am auditing this course just for knowledge the teacher does not want to waste the
Say the only tool you have available to you is a pocket calculator which performs addition, subtraction, multiplication, and division, accurate to 15 decimal places. Explain a practical way to compute: Integral from 0 to 1 of e^[-(x^2)] to within an error less than 10^-8. Prove that the method works.
1. Find the indefinite integrals 2. Suppose that the rate of increase of paper production in the US for recent year is given approximately by... (see attachment)
Please evaluate the integral attached
34.8 (a) Use integration by parts to evaluate 1 ∫ xּarctan x dx. 0 Hint: let u(x) = arctan x, so that u′(x) = 1/(1+x2). (b) If you used v(x) = x2/2 in part (a), do the computation again with v(x) = (x2+1)/2. This interesting example is taken from J. L. Borman[6].
Evaluate the integral from 0 to inf. of [cos(3x)-cos(5x)]/x^2 dx
Evaluate the integral from 0 to infinity of X^2/(X^4+2X^2+1) dx
Q. Show that f is Riemann-integrable. What is ∫[0,1] f(x)dx? (Hint: What's the set of discontinuity of f? Does it have Vol1-zero?) Please see attached for full question.
Please see the attached file for the fully formatted problems. Q: Suppose and are continuous and F(x) = Let (a) prove that f'(x) + g'(x) =0 for all x (b) Prove that f(x) + g(x) = /4 for all x. Deduce that
Please see the attached file for the fully formatted problem.