In Problems 9 to 12, evaluate the definite integrals using the Simpson's rule, giving the answers correct to 3 decimal places. -π/2 9. f/² √sinx dx. (Use 6 intervals) [1.187]

Q: Evaluate the definite integral: 3 ƒ³₁ x(x² + 1)³/² dx. Give your answer correct to 2 decimal places.

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Q: 5. Perform the following indefinite integral. Verify your result by taking its derivative: [(cos 2x-…

A: We use substitution method to solve this integration

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A: Some properties of integration  I=∫g'(x)f(g(x))dx, put  t=g(x)   then I=∫f(t)dt ∫axdx=axloga+C

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Q: solve the differenctil equation by undtermeind coefficients y'' +2y = -18x2e2x   y(x) = ?

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Q: (7) sin √x dx. (First substitution, then by parts)

A: The solution for the given integral is as follow.

Q: Help me find the indefinite integrals and evaluate the definite integrals. Change of variable if…

A: Step 1:Step 2:Step 3:Step 4:Step 5:

Q: 3. Use the fundamental theorem of calculus to find the exact value of the definite integral. Show…

A: Definition used -                 Power rule of integration -                       ∫xndx…

Q: 1 dx x² + x r2

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Q: | Va? – 4 x² – 4 dx x2

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Q: Inx dx where x>0. 1

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Q: For items 9 and 10, refer to f - (x*+1)dx x*+2x3+x² 9. What is the degree of the polynomial in the…

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Q: B. Evaluate the definite integral using the Simpson's rule, giving the answer correct to 3 decimal…

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Q: Use geometry to evaluate the following definite integrals. Sketch a graph of th function, show the…

A: 1. ∫048-2xdx 2. ∫-422x+4dx 3. ∫0416-x2dx We have to evaluate the given integrals and also sketch the…