Post a New Question

calculus

posted by .

using the fundamental theorem of calculus what is the derivative of the definite integral from x^3 to sqrt x of (sqrt t) sin t dt

  • calculus -

    The first fundamental theorem of calculus states that if f(x) is continuous, real and defined on [a,b], and
    F(x)=∫f(x)dx from a to b
    then
    F(x) is continuous on [a,b] and differentiable on (a,b), then
    F'(x) = f(x).

    In this case f(t)=sqrt(t)sin(t), definite integral is calculated from x³ to √(x).

    Thus if the above theorem to apply, t must be non-negative, which implies that x>0.

    If the condition is satisfied, then f(t) is continuous and defined on [0,∞], and consequently F'(t) = f(t).

  • calculus -

    Yoto

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus - Second Order Differential Equations

    Posted by COFFEE on Monday, July 9, 2007 at 9:10pm. download mp3 free instrumental remix 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 …
  2. 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 …
  3. 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?
  4. calculus

    Calculate definite integral of dx/(x^4 * sqrt(x^2 + 3)) Over (1,3) I start with the substitution x = sqrt(3)*tan t so: sqrt(x^2 + 3) = sqrt(3) * sec t dx = sqrt(3) * sec^2 t dt x^4 = 9 * tan^4 t The integral simplifies to: = dt/(tan^3 …
  5. Maths Calculus Derivative Integral - Urgent Please

    Use 2nd Fundamental Theorem of Calculus to find derivative of f(x) = integral of 2x^2 (at the top) to x-5 (at the bottom) of square root of Sin(x)dx
  6. Calculus

    "Leave the answer as a definite integral, but indicate how it could by evaluated by using the fundamental theorem of calculus." I solved the problem to a definite integral. Proceeding via the fundamental theorem, would involve finding …
  7. ap calculus

    Which of the following definite integrals gives the length of y = e^(e^x) between x=0 and x=1?
  8. Calculus Fundamental Theorem

    Evaluate the definite integral. function: (t+8)(t^2+3) with respect to variable t lower limit: -sqrt(2) upper limit: sqrt(2)
  9. Calculus 2 (Differential Equation)

    How would you solve the following problem explicitly?
  10. Calculus1

    find the derivative using fundamental theorem of calculus integral of sin^3tdt from e^x to 0

More Similar Questions

Post a New Question