Expand the integral $\int\left(\cos\left(x\right)^2-\cos\left(x\right)^{4}\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
The integral $\int-\cos\left(x\right)^{4}dx$ results in: $\frac{-\cos\left(x\right)^{3}\sin\left(x\right)}{4}-\frac{3}{4}\left(\frac{1}{2}x+\frac{1}{4}\sin\left(2x\right)\right)$
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more
The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.