Friday

September 19, 2014

September 19, 2014

Posted by **adela** on Sunday, January 2, 2011 at 4:39am.

- calculus -
**MathMate**, Sunday, January 2, 2011 at 8:48amThe 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 -
**Ooooooo**, Friday, October 12, 2012 at 6:43pmYoto

**Answer this Question**

**Related Questions**

Calculus - "Leave the answer as a definite integral, but indicate how it could ...

Calculus Fundamental Theorem - Evaluate the definite integral. function: (t+8)(t...

Calculus - Please look at my work below: Solve the initial-value problem. y'' + ...

calculus - Calculate definite integral of dx/(x^4 * sqrt(x^2 + 3)) Over (1,3) I ...

ap calculus - Which of the following definite integrals gives the length of y = ...

Math/Calculus - Solve the initial-value problem. Am I using the wrong value for ...

Maths Calculus Derivative Integral - Urgent Please - Use 2nd Fundamental Theorem...

Calculus - Second Order Differential Equations - Posted by COFFEE on Monday, ...

Calculus - Find the volume of the solid whose base is the region in the xy-plane...

Calculus - Evaluate the indefinite integral: 8x-x^2. I got this but I the ...