Find the area of the region bounded by the graphs of $y = 1$ and $y = \cos^2(x)$ from $x = 0$ to $x = π$.
$a. 0.785$
$b. 3.142$
$c. 2.576$
$d. 1.571$
I graphed it but I'm not sure what to do next. Please help
Find the area of the region bounded by the graphs of $y = 1$ and $y = \cos^2(x)$ from $x = 0$ to $x = π$
-1
$\begingroup$
calculus
integration
area
curves
-
1You tagged the question with "integration". You should show your attempt on the question with integration. – 2017-02-08
-
0I knew that integration had to be used, I just wasnt sure how to apply it, which is why I graphed it. – 2017-02-08
2 Answers
0
When you mean $\cos^2\left(x\right)$:
$$\int_0^\pi1\space\text{d}x-\int_0^\pi\cos^2\left(x\right)\space\text{d}x=\frac{\pi}{2}\approx1.570796326794897$$
0
Use the double-angle formula:
$$ cos (2x) = cos^2(x) - sin^2(x)$$ $$ 1 = cos^2(x) + sin^2(x)$$
Add those two equations and you get $cos(2x) + 1 = 2 cos^2(x)$
Divide by 2 and you get the handy reduction formula
$$cos^2(x)= \frac{cos(2x) + 1}{2} $$
Substitute this in your integral and with a simple substitution you can do the rest of the integral.