Question

Let h be the function defined by h(x) = ∫(x to π/4) sin(2t) dt.

Answer 1

The function h(x) is the integral of sin(2t) from x to π/4, and it is equal to 0.5*cos(2x).

Step-by-step explanation:

The function h(x) is defined as the integral of sin(2t) from x to π/4. To evaluate this integral, we can use the anti-derivative of sin(2t), which is -0.5*cos(2t). So the integral of sin(2t) dt is -0.5*cos(2t) + C, where C is the constant of integration.

To evaluate h(x), we need to find the definite integral from x to π/4. Substituting the limits of integration into the anti-derivative, we get:

h(x) = -0.5*cos(2*π/4) - (-0.5*cos(2x)) = -0.5*cos(π/2) + 0.5*cos(2x) = 0.5*cos(2x).