Finding an Indefinite
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Calculus
- Evaluate the integral dx (a) Find and use a substitution, which leads to integration of a rational function. (b) Is the obtained rational function proper or improper? If improper, use the long division to simplify. Do not skip any steps. (c) Use partial fraction decomposition to reduce the rational function to a sum of elementary rational functions. Show all the steps. (d) Evaluate the integral (do not forget to return to the original variable).arrow_forwardCalculus IIarrow_forwardAlgebra Suppose that the function p(x) approximates the function f(x) with a maximum error of ε over the interval [a, b]. Then what is the error for the approximation of the integral [a,b] p(x)dx for the integral [a,b] f (x)dx.arrow_forward
- 53-73 Evaluate the definite integral.arrow_forwardConsider the graph of the function f(x) shown below. a) Estimate the integral ∫70 f(x)dx ≈ ____________________ (thats not a 70, the 7 is at the top of the integral sign and the 0 is at the bottom of the integral sign) b) If F is an antiderivative of the same function f and F(0)=35, estimate F(7):F(7)≈__________________________arrow_forwardpls find the derivitvearrow_forward
- Calculus 1, 135:01-05, S20 Ant Quiz: Quiz 11 This Question: 3 pts 4 of 8 (2 complete) Evaluate the following integral using the Fundamental Theorem of Calculus. 12 | (5- x)(x- 12) dx 12 343 | (5- x)(x- 12) dx = 6 5 (Type an exact answer.) (ц) Morearrow_forwardHand writingarrow_forwardEvaluate the definite integral X -1 1 + x² + x4 (a) [¹ 1 હૂંz, √x, (b) [¹² (x² + 3)(2x + 1)dx, (c) [²x²e²³ dæ dx -1 -1 222arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning