In 8 et dx 64 + e2x In(1/8)

Q: Evaluate the improper integral 2x dx, if it exists. (x² + 81)2

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Q: Evaluate the following integral. e5 dx 3x In x In (In x)

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Q: The integral of 3^4x dx is equal to * O 4^4x / In3 + C O 3^4x/In12 + C O 3^4x / In27 + C O 3^4x /…

A: SOLUTION-

Q: Evaluate the definite integral.

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Q: Consider the following integral: (³ In(2x) dx.

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Q: in S 0 n soo

A: Here we have to Evaluate the double integral

Q: Compute the definite integral.

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Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx 3+ (3e)3 + cosh2x A + C 2+2ln3 (3e)3 + sinh2x…

A: The integration are

Q: 1) Use Simpson's Rule with n=4 to calculate S x² dx.

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Q: Find the indefinite integral ∫ e2x/ (4 + e4x)   dx

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Q: Evaluate the integral. 5x dx -5x 5x e

A: Given,  ∫5x e-5xdx

Q: In 2 ety dy dx In 3 1-

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Q: Evaluate the integral. In3 3e2x dx In3 3e 2x dx = 0

A: As we know that; ∫a·fxdx=a·∫fxdx And ∫eaxdx=eaxa+C From the given problem: I=∫0ln33e2xdx

Q: Show that (In kx) dx (In x), where x > 0 and k is a positive dx real number.

A: ddxln kx=ddxln x, where x>0 & k is a positive real number.

Q: d 1. -x In x = In x +1 dx

A: the given expression is: dxlnxdx=lnx+1

Q: Test for vergances of fallowing Cor +oo Σ n=1 Jn² +n

A: Limit comparison test : Suppose we have two series ∑n=1∞ an and ∑n=1∞ bn where an,bn≥0 for all n…

Q: Evaluate: dx. x-2 A) In 3 - In(-2). B) The integral diverges. C) In 3 - In 2. D) - In 3 + In 2. In 3…

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Q: In|In x| + C 2.STinx dx x In x 1 3/x +C 3. S dx

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Q: - (In /3) /4 4 e4x dx 1 + e8x

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Q: Evaluate the integral. S. 4 x* - 3 dx 14 4 x* - 3 dx = 14

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Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx

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Q: In(3) e Ver +1 dx In(2)

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Q: Find * In(x² + 2x + 2) dx (x + 1)² In|1 + (x + 1)²| x +1 In|1 + (x + 1)2| x + 1 + 2tan-(x + 1) +c…

A: I am attaching image so that you understand each and every step.

Q: 5. Evaluate x + v1 – x² dx by interpreting it in terms of areas.

A: We have to consider it as sum of two functions.

Q: Evaluate integral of dx/x+2 from -6 to -10 Choices: •In 2 •In 3 •21/3 •1/2

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Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 2+In3 +C (3e)3+cosh2x B) 2+2ln3…

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Q: 1. (a) Prove the following. | (In x)"dx = x(In x)" – n (In x)-' dx

A: To prove that 1.a. ∫lnxndx=xlnxn-n∫lnxn-1dxb. Using 1.a compute the following      ∫lnx3dx

Q: Evaluate the integral x - 4 dx. x+6 0. 3. 2 10 In 4 In 8 2 10 - In 6 4 2 10 In O 2 10 In 48

A: which option?

Q: evaluate using the appropriate method or combination of methods.

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Q: 1 dx. Evaluate *(In.x) 4

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: Evaluate (а) S In(2.x + 2)dx -1

A: Given:          (a): ∫−11ln(2x+2)dx

Q: If In(ax)dx = 4, then a ( In(ax)dx %3D 1 4

A: we have to find the value of a

Q: Evaluate the integral: Só(5 + 4x) dx dy O 18 O 36 O 2 O 4

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Q: 2 Evaluate the integral: 3x(5-3x dx

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Q: Evaluate the integral. . 4 1) x In 2x dx 1

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Q: Evaluate 1- x? dx 0. by Simpson's rale with n=5

A: Here fx=x1-x2 The interval is 0,1 and n=5. Hence the interval is divided into 5 equal parts.…

Q: Compute the integral 4x /5 – e2¤ dx. e

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Q: (b) Evaluate In(x) dx 1

A: The given integral is divergent.

Q: d) Prove the results of the integrals 3 dx = 2+ In (2)– 4 [In (5)– In (3)]. x² +3x +2

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Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 +C B (3e)3+cosh2x 2+2ln3…

A: This question can be solved using integration by substitution.

Q: In Evaluate the integral: Sé e x²+3x-7 x-2 dx

A: Option (b) x22+5x+3ln|x-2|+C

Q: Integrate 2 In(11x) -dx . a) In (æ)? 2 11 + C b) None of these c) In (11æ)² + C 2 d) In (11æ)² + C…

A: topic - indefinite integral

Q: S az lnz (In z + 1)dz z In

A: ∫azlnzlnz+1 dz Put, z lnz=u⇒1·lnz+1z·z=dudz⇒lnz+1=dudz⇒lnz+1 dz=du

Q: 7. Evaluate the integral x4 6x5 1 dx

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Q: 16. Evaluate x + v1- x² dx by interpreting it in terms of areas.

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Q: 8) The integral |4* dx is equal to 5x 5x 5x - +C C. In 5 А. -+C In 4 В. +C 5in4 D. +C 4 In5

A: Given ∫45x dxSubstitute u=5x → dudx=5→dx=15du=15∫4u duNow solving ∫4u duApply Exponential rule: ∫au…

Q: If In |(In x)" dx, show that In = x(In x)" – n.Ip-1- Hence find nx)* dx.

A: I am going to prove the given identity by using integration by parts and then use this identity to…

Q: 5 + In x Evaluate dx. x(1 – In æ)

A: We need to evaluate the integral - I=∫5+ln3xx(1-lnx)dx We will solve it by substitution method.

Q: Evaluate the integral. „ 3X + 7 e ~×) dx , 3× + 7 e ~×) dx =

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Q: Evaluate the double integral : 9 dy dx 36 – 12 - 12 -36

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.