2. Given: L//L2, L3//L4 Prove: < 2 E< 4 L2 2. Ls LA

Q: ot) Evaluate the integral 9 L₁ (1x) — 4) da (|x|- dx - -7 using the net area of a region. Give the…

A: Here we have given an integral:

Q: 91/ Find y 1. Y rx) 2/x tanh Cr 2. Y-Cosh' (2Jx tI ) (2Jx+I

A: Find derivative

Q: 9. Evaluate #/ Vcos(t4) +t+ 4 dt. Give a reason for your answer.

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Q: O Find absolute extrema for f(x)= x*-6x² +9x +l in terval [0,5] Gn

A: Given that fx=x3-6x2+9x+1To find : absolute extrema on interval  0,5Solution…

Q: Use integration by parts to verify the reduction formula.

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Q: Prove LHS=RHS

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Q: A die is thrown 8 times. Let X = number of 3's. Find P ( X> 2). %3D

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Q: Prove that Ek=0 C) 7n-k . 2k = 32n %3D

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Q: d 3(In(In x))? 13. - (In(In x)}³ dx x In x

A: According to the question, we have to prove the statement ddxlnlnx3=3lnlnx2xlnx. The derivative of a…

Q: Using the definite integral, calculate: n 2 3 lim + 2(;) i=0

A: See the solution.

Q: 3.29. Let A = 1 -2 0 21 4 0 If A is invertible find A-¹. Otherwise show that it is not invertible.…

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Q: S- dx = In]x| – e* + C 5. S 2²+3*dx = 4| + C In 8

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Q: -e lim te Int - 1

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Q: Evaluate the integral * In 2 tanh 2x dx

A: We have to find Integral of given function.

Q: The Area between k*x3 and k*sin (x) is 2. What is the value of k?

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Q: 15) S secx * ln(tanx + secx) dx 15) ſ

A: we have to evaluate Now use the method of substitution Hence the integration becomes

Q: Let f f(x) dx = 11 and ₁ f(x) dx = -15 Evaluate the following integrals. So 5 f(x) dx So f(x) dx Use…

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Q: Estimate the area under the graph of f(x) = x² + 4x + 1 over the interval [1, 6] using five…

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Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts: ∫sinn x dx=-sinn-1 x cos…

Q: Steb by step

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Q: 75. Use the Comparison Theorem to show that x* dx, x* dx < х ах x' dx <

A:

Q: Q1:- Find the area bounded by the curve F(X)=(-X^2)+8X-7 and the x-axis between the function’s…

A: Given f(x) =-x2+8x-7

Q: 3) f(x) = 2x + 5, on the interval [–1,4]. Use RRAM and five sub-intervals to approximate the area…

A: Note:  According to the guidelines issued by the company we should answer only one question, please…