Exercise
$\int_o^{\frac{\pi}{2}}\left(q\left(1-senx\right)^2-r\left(1+cosx\right)\left(1-senx\right)\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function q(1-sin(x))^2-r(1+cos(x))(1-sin(x)) from o to pi/2. A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: (a-b)^2=a^2-2ab+b^2. Multiply the single term q by each term of the polynomial \left(1-2\sin\left(x\right)+\sin\left(x\right)^2\right). Multiplying polynomials -1 and 1+\cos\left(x\right). Multiplying polynomials -1-\cos\left(x\right) and 1-\sin\left(x\right).
Integrate the function q(1-sin(x))^2-r(1+cos(x))(1-sin(x)) from o to pi/2
Final answer to the exercise
$-qo+\frac{\pi }{2}q-2q\cos\left(o\right)+q\left(\frac{\pi }{4}-\frac{1}{2}o+\frac{1}{4}\sin\left(2o\right)\right)+ro+\left(-\frac{\pi }{2}\right)r+r\left(-1+\sin\left(o\right)\right)+r\cos\left(o\right)+\frac{-\cos\left(2\cdot \left(\frac{\pi }{2}\right)\right)r}{4}-\frac{-r\cos\left(2o\right)}{4}$