This concept applies the Fundamental Theorem of Calculus to evaluate definite integrals of the tangent function, using a known antiderivative (the natural log of the absolute value of cosine) evaluated at the bounds, rather than computing a Riemann sum directly. It also illustrates a complementary geometric technique: recognizing that the definite integral of an odd function over a symmetric interval about zero equals zero due to cancellation of positive and negative signed areas. This situates the topic within definite integration theory in single-variable calculus, where the Fundamental Theorem of Calculus provides a computational alternative to the limit-of-Riemann-sums definition.
This concept applies the Fundamental Theorem of Calculus to evaluate definite integrals of the tangent function, using a known antiderivative (the natural log of the absolute value of cosine) evaluat…