Post a New Question

Calculus

posted by .

Given that \displaystyle \int_0^4 x^3\sqrt{9+x^2} dx = a, what is the value of \lfloor a \rfloor?

  • Calculus -

    Put x = 3 sinh(t), then:

    Integral from 0 to 4 of

    x^3 sqrt{9+x^2} dx =

    Integral from 0 to arcsinh(4) of

    3^5 sinh^3(t) cosh^2(t) dt =

    3^5 Integral from 0 to arcsinh(4) of

    sinh(t) [cosh^2(t) - 1] cosh^2(t) dt =

    3^5 Integral from 0 to arcsinh(4) of

    [cosh^2(t) - 1] cosh^2(t) dcosh(t)

    Putting cosh(t) = u gives:

    3^5 Integral from 1 to sqrt(17) of

    [u^2 - 1] u^2 du =

    3^5 {sqrt(17)[1/5 17^2 - 1/3 17] + 2/15 }

    You then need to round this off to below.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Please look at my work below: Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2, e^(8*0)*(c1*cos(0)+c2*sin(0))=c2=2 …
  2. Math/Calculus

    Solve the initial-value problem. Am I using the wrong value for beta here, 2sqrt(2) or am I making a mistake somewhere else?
  3. calculus

    It is known that if m <= f(x) <= M for a <= x <= b, then the following property of integrals is true. m(b-a) <= int_a^b f(x)dx <= M(b-a) Use this property to estimate the value of the given integral. ?
  4. Calculus

    Given that \displaystyle \int_0^4 x^3\sqrt{9+x^2} dx = a, what is the value of \lfloor a \rfloor?
  5. Algebra

    What is \left \lfloor ( 3 + \sqrt{5} ) ^3 \right \rfloor?
  6. Calulus

    Given \displaystyle \int_0^{\frac{3\pi}{2}} x^2\cos x \, dx = a - \frac{b\pi^2}{c}, where a, b and c are positive integers and b and c are coprime, what is the value of a + b + c?
  7. Trigonometry

    ABC is a non-degenerate triangle such that 2\sin \angle B \cdot \cos \angle C + \sin \angle C = \sin \angle A + \sin \angle B, what is the value of \lfloor 100 \frac {AC}{AB} \rfloor ?
  8. Simple Calculus

    Evaluate \displaystyle \lim_{x \to 0} \frac{\sqrt{2}x}{\sqrt{2+x}-\sqrt{2}}.
  9. calculus

    a. The value of \displaystyle \int_{-2}^{-1} \frac{14}{ 4 x } dx is b. The value of \displaystyle \int_{1}^{2} \frac{14}{ 4 x } dx is
  10. Calculus check

    Given f(x)=4+3/x find all values of c in the interval (1,3) that satisfy the mean value theorem. A. 2 B. Sqrt(2) C. Sqrt(3) D. +or- sqrt(3) E. MVT doesn't apply I got C

More Similar Questions

Post a New Question