Evaluate the definite integral. ∫√3x+6dx upper limit of 1 and lower limit of 0

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A: Express the limit as a definite integral on the given interval.

Q: 1. Approximate the value of each of the following definite integrals using: i. Trapezoidal Rule

A: As per Bartleby's answering policy, we can answer only one question, so kindly post the remaining…

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A: Given  ∫-∞∞x31+x8dx=?

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A: we integrate the given function . see 2nd and 3rd step.

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Q: Use the definition of the definite integral a sum to evaluate | (2 – 3r)² dxr. as a limit of

A: Given:           I=∫-112-3x2dx To Find I using definite integral as a limit of sum:

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Q: Evaluate the definite integral

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Q: Evaluate the definite integral by the limit definition

A: Given that: The integral is ∫14 4 x2 dx .

Q: (a) '8 dx 2

A: (a)∫268 dx=[8x]26We know that ∫k dx=kx+C            = 8*6 - 8*2            = 32

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Q: Evaluate the integral, if it exists.    ∫ (8 x3  +3x2) dx

A: Given- ∫8x3+3x2dx To evaluate- The above integral. Formula used- The power rule, ∫xndx=xn+1n+1+C,…

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Q: Express the limit as a definite integral on the given interval. x; In(1 + x3) Ax, [2, 3] lim 3 dx

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Q: sech(In x) 9) dx

A: ∫15 sechln xxdx

Q: Evaluate the definite integral by the limit definition. L (x² + 4) dx X 31

A: use the limit formula for integration

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Q: Express the limit as a definite integral on the given interval. lim Ax [О, 6] 9 + X; i = 1 dx

A: The answer is found in step-2

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Q: Q5. Apply the mean value theorem for integrals to evaluate e Lim -dx. 2 + CoS x

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Q: Find the indefinite integral ∫xsinx2 dx

A: Given: The integral ∫xsinx2dx, To evaluate: The given indefinite integral.

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A: I am going to solve the given problem by using some simple calculus to get the required result.

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A: The given problem can be solved as-

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A: Given: ∫031-2x2dx

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Q: Find the indefinite integral ∫x+1√xdx.

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Q: Use the Simpson's Rule to evaluate the integral f x|x²dx

A: Please post the multiple questions separately.Here I answered 1st question  as per our policy.

Q: Evaluate the definite integral by the limit definition

A: ∫268dxFormula:∫abcdx=cxab=cb-a   , where c is any constant.