6. Evaluate any 5 of the following 6 integrals. (a) 12 dx 1 (b) (c) cos(50) de (e) [x²e² dr (d) (f) √2+1 dz | dx [arcsin a da

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A: Consider the following revenue function, where R(x) is measured in dollars. R(x)=110x-0.1x^2 a. Use…

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A: Problem statement is not given so considering unit conversion by given options.

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Q: #6

A: Topic:- application of integration

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A: Here (g∘f)(2)=g(f(2))But f(2)=3(g∘f)(2)=g(3)and g(3)=6Therefore(g∘f)(2)=6

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A: Given problem:- Let f(x) = 2x3 - 7x2 + 4x .   a. On what interval(s) is f'(x) > 0?   b. On what…

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A: Use derivative for finding the line integral.

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A: Explanation of the answer is as follows

Q: 7. Use Lagrange Multiplier to find the maximum and minimum values of the function f(x, y) = x²y…

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Q: Find the arc length L of the graph of r(t). r(t) = 9 cos(t)i +9 sin(t)j + tk, 0≤t≤ 2π

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Q: 5. By the Fundamental Theorem of Calculus (Newton-Leibnitz Theorem) √² + x² d VX evaluate

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Q: 1) Calculate the following integrals 1_dx a) S 4x²+25

A: Given; I=∫14x2+25dx    .....(1)   As we know that; ∫1x2+1dx=tan-1x+C

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Q: 3. Evaluate the double integral: ²₂2(x+3) dy dx 4. Evaluate the triple integral: ₂ dx dy dz Z

A: Topic:- multiple integration

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A: A loaf of bread can be modeled by a rectangular prism topped with half a right cylinder. Katherine…

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Q: ^ du 1 1+2 Sinn

A: Solving the given integral using the substitution method Also using the formula for the integration…

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Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

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A: This integration can also be found from area under the curve .