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Evaluating a Line
C: boundary of the region lying between the graphs of the circle
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Calculus
- Line integrals Use Green’s Theorem to evaluate the following line integral.Assume all curves are oriented counterclockwise.A sketch is helpful.arrow_forwardsinx cosx - e +e sinx +* The integral dx may be written as me nsinx +px+ qe™ + C, sinx where m, n, p, q, r, and C are constants not equal to zero. Evaluate m+n+p+q +r.arrow_forwardTutorial Exercise Use the form of the definition of the integral given in the theorem to evaluate the integral. (1 + 5x) dx -2arrow_forward
- Green's Theorem, answer:arrow_forwardUsing Trigonometric Substitution In Exercises 11–14, find the indefinite integral using the substitution x = 2 tan 0. 11. 4 + x² dx 12. 4/4 + x dxarrow_forwardDirections: Using Fundamental Theorem of Calculus (FTOC), compute the following definite integrals. 1. ²(3x² - 4x + 1)dx 3. f sec² x dx 5. J₂lx - 3|dx 2. (x²-2x) dx 4. ², (4x + 5) dxarrow_forward
- The figure shows the sales growth rates under different levels of distribution and advertising from a to b. Set up an integral to determine the extra sales growth if $3 million is used in advertising rather than $2 million. (Use f for f(x), g for g(x), and h for h(x).) $4 Million advertising $3 Million 8 advertising $2 Million h advertising a Distribution dx Need Help? Read It Sales Growth Ratearrow_forwardArea Function a) Find the formula for the area function, A(x), represented by the integral. b) Use that formula to find both A(t) and A(2t). c) Graph f(t) = sin (;t) and shade the area for the interval [0, 27]. d) Graph A(x) on the same graph and plot the point (2r, A(2n)). e) What is the relationship between parts (c) and (d)? sin dtarrow_forwardSurface Area The roof over the stage of an open air theater at a theme park is modeled by f(x, y) = 25[1 + e−(x2+y2)1000 cos2(x2 + y2/ 1000 )] where the stage is a semicircle bounded by the graphs of y = √502 − x2 and y = 0. Use a computer algebra system to approximate the number of square feet of roofing required to cover the surface.arrow_forward
- Calculus 1 (a) Evaluate the indefinite integral u(1+u) du. 1 1+ u-u Hint: u(1 + u) u(1+u) * (b) Using a substitution, and your answer in part (a), evaluate the 1 dx. integral S indefinite integral 1 + exarrow_forwardCalculus 11th Edition - Ron Larson Chapter 3.9 - Differentials Find the tangent line approximationT to the graph of f at the given point. Thencomplete the table.arrow_forwardsinx +e sinx +x COSX -e The integral dr may be written as me nsinx + px + qe"+ C, where m, n, p, q, r, and Care constants not sinx equal to zero. Evaluate m +n+p+q+r.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage