MHB Find Upper Limit of Integral: "Integration Please Help?

AI Thread Summary
To find the upper limit of the integral for the function f(x) = 2sin(x) where the area between the curve, the line x = a, and the x-axis equals 1, the equation 2∫0^a sin(x)dx = 1 is set up. By simplifying, the equation becomes ∫0^a -sin(x)dx = -1/2. Applying the Fundamental Theorem of Calculus leads to the expression cos(a) - 1 = -1/2. Solving this gives cos(a) = 1/2, resulting in a = π/3. The solution for the upper limit a is therefore π/3.
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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.
 
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Hello jasna,

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

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

Divide through by $-2$:

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

On the left, apply the FTOC:

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

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

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

$$a=\frac{\pi}{3}$$
 
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