A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing

This Question is Open

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0Do you know the Fundamental Theorem of Calculus?

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.0note that \(\int cos x dx= sin x +C\)

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0It says\[\int\limits_{a}^{b}f(x)dx=F(a)F(b)\]In this case this means: (see also the answer of Shadowys)\[\int\limits_{\frac{ \pi }{ 4 }}^{\frac{ \pi }{ 4 }}cosxdx=\sin(\frac{ \pi }{ 4 })\sin( \frac{ \pi }{ 4 })=\frac{ 1 }{ 2 }\sqrt{2}\frac{ 1 }{ 2 }\sqrt{2}=\sqrt{2}\]

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0F is called a primitive function of f. It means: F'(x) = f(x). So the Fundamental Theorem makes integrating (= calculating an infinite sum of infinite small numbers  very hard!) much easier: if you can find a primitive F of f, you're done. In the case of cos(x) this is simple: (sinx)' = cos x, so F(x) = sinx.
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.