Question

Let $F(x) = \int_{\pi}^{x} t \cdot \sin(t) dt$. (a) Find $F(\pi)$. (b) Find $F'(x)$. (c) Find $F'(\frac{\pi}{2})$. (d) Express $F(2 \cdot \pi)$ as an integral of $t \cdot \sin(t)$. (e) Express $-F(x)$ as an integral of $t \cdot \sin(t)$.

          Let $F(x) = \int_{\pi}^{x} t \cdot \sin(t) dt$.
(a) Find $F(\pi)$.
(b) Find $F'(x)$.
(c) Find $F'(\frac{\pi}{2})$.
(d) Express $F(2 \cdot \pi)$ as an integral of $t \cdot \sin(t)$.
(e) Express $-F(x)$ as an integral of $t \cdot \sin(t)$.

Let F(x) = ∫π^x t ·sin(t) dt.
(a) Find F(π).
(b) Find F'(x).
(c) Find F'((π)/(2)).
(d) Express F(2 ·π) as an integral of t ·sin(t).
(e) Express -F(x) as an integral of t ·sin(t).

Added by Nicholas H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Leon Druch

08/10/2021

Step 1

So, F(\pi)=\int_{\pi}^{\pi} t*sin(t)dt. Show more…

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Let F(x)=int_(pi )^x t*sin(t)dt. (a) Find F(pi ). (b) Find F^(')(x). (c) Find F^(')((pi )/(2)). (d) Express F(2*pi ) as an integral of t*sin(t). (e) Express -F(x) as an integral of t*sin(t). x t. sin( TT Let F(x)= dt (a) Find F(T) (b) Find F'(x TT (c) Find F 2 (d)Express F(2Tt) as an integral of t sin(t) (e) Express -F(x) as an integral of t.sin(t) .