math

The definite integral of cos(theta) from 0 to pi/2 is equal to 1. This is derived from the result of the Fundamental Theorem of Calculus, which states that if f is continuous and differnetiable on the interval [a, b], then the definite integral of f from a to b, denoted as ∫abf(x)dx, is equal to the value of F(b) - F(a), where F is the antiderivative of f. In this case, the function f(theta) = cos(theta) is continuous and differentiable on the interval [0, pi/2]. Taking the antiderivative of f yields F(theta) = sin(theta), and therefore we can calculate the definite integral with F(pi/2) - F(0). Since sin(pi/2) = 1 and sin(0) = 0, the result is 1.