Consider the functions f and g, where f (x) = 6 sin x cos² x and g(t) = ∫^t₀ f (x) dx.(a) Use a graphing utility to graph f and g in the same viewing window.(b) Explain why g is nonnegative.(c) Identify the points on the graph of g that correspond to the extrema of f.(d) Does each of the zeros of f correspond to an extremum of g? Explain.(e) Consider the function

Use a graphing utility to graph h. What is the relationship between g and h? Verify your conjecture.

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- SP1₂² π/2 h(t) = f(x) dx.