Final answer:
To evaluate the integral ∫(20sin10(x)) dx using Wallis's formulas, you can simplify it by applying the formula for integrals of powers of sine. Then, evaluate each integral separately to find the final result.
Step-by-step explanation:
To evaluate the integral ∫(20sin10(x)) dx using Wallis's formulas, we can use the formula:
∫sin^n(x)dx = (n - 1)/(n) * ∫sin^(n-2)(x)dx - (1/n) * ∫sin^n-2(x)dx
In our case, n is 10, so we can use Wallis's formulas to simplify the integral. The integral becomes:
∫(20sin10(x)) dx = (10 - 1)/(10) * ∫sin^8(x)dx - (1/10) * ∫sin^10(x)dx
Now you can evaluate each of these integrals separately using integration techniques, such as substitution or trigonometric identities, and then calculate the final result.