MATH 1131Q Lecture Notes - Lecture 14: Differentiable Function, Antiderivative
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Math 1131q , lecture 14 , sections 5. 5 / 6. 1. If u = g(x) is a differentiable function whose range is an interval i and f is continuous on i, then. X^3 (7 + x^4)^6 dx u = 7 + x^4 du/dx = 4x^3 du/4 = x^3 dx divide by 4 , multiply by dx. = 1/28 (7 + x^4)^7 + c substitute u from original equation pull the to the outside of the integral take antiderivative of integral. If g"(x) is continuous on [a , b] and f is continuous on the range of u = g(x), then. Find the area of the region enclosed by the given curves. y = e^x , y = x^2 , x = -1 , x = 1. = [ e^1 - e^-1 ] - { [ - 1 ] - [ - + 1 ] } = e^1 - 1/e - [ - 2 ]
