MAT136H1 Lecture Notes - Antiderivative

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: all

Document Summary

Question #5 (medium): using series to approximate definite integral. Same as evaluating the indefinite integral, definite integral follows the same procedure: first converting the function inside the integral into an infinite series expression. Then put inside the definite integral, then work out the anti-derivative form of the series. Then given the error bound, test a couple of terms that fall within the error range, then add the terms up to but excluding that tested term as an approximation to the definite integral. Use series to approximate the definite integral to within the indicated accuracy. The function inside the definite integral need to be expressed as infinite series first: ( ) Now this can go inside the definite integral: The second term is outside the error bound, but the third term.