Find Upper Limit of Integral: "Integration Please Help?

[MarkFL]

Here is the question:

Integration please help?

f(x)=2sinx

a is somewhere between 0 and π
the area between f(x), a=x and axis equals 1
find a?

I have posted a link there to this thread so the OP can view my work.

 

[MarkFL]

Hello jasna,

We are being asked to solve the following equation for $a$:

\(\displaystyle 2\int_0^a \sin(x)\,dx=1\)

Divide through by $-2$:

\(\displaystyle \int_0^a -\sin(x)\,dx=-\frac{1}{2}\)

On the left, apply the FTOC:

\(\displaystyle \left[\cos(x) \right]_0^a=-\frac{1}{2}\)

\(\displaystyle \cos(a)-1=-\frac{1}{2}\)

\(\displaystyle \cos(a)=\frac{1}{2}\)

\(\displaystyle a=\frac{\pi}{3}\)