Use Gauss-Legendre formula to evaluate the integral e¯x*dx_with n = 3.

Q: x3 . In x dx

A:

Q: 2 In(x) 1 dx

A: Consider the provided integral, ∫01 2lnxxdx Evaluate the above integral.

Q: Use integration tables to find or evaluate the integral.

A: We have to evaluate the integral: ∫x4+5x2dx Assuming, t=4+5xx=t-45 Differentiating,…

Q: In V3 dx 1+e2cx

A:

Q: Compute the integral by rewriting the integrand: Integral of (1 divided by x7 times the square root…

A: Please refer to the image below

Q: Use integration by parts to evaluate the integral: In(s)ds

A: Given, To Evaluate

Q: dx

A: Consider the integral

Q: Evaluate the integral So So -8 e dady by reversing the order of integration.

A:

Q: xarctanx dx

A: Product Rule of integration : ∫u.v dx = u∫vdx - ∫(dudx∫v dx)dx darc tanxdx = 11+x2 ∫ xn dx =…

Q: Use Simpson's Rule to approximate the given integral with the specified value of n. Integral sign…

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Q: Evaluate the integral in terms of Beta function: ∫x^12(1−x)^16 dx    limit: 0 to 1

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Q: In(x) dx =

A: To find:∫lnxx5dx

Q: Evaluate the integral by reversing the order of integration. 6ely dy dx

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Q: 4 dx x4-1

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Q: dx Evaluate the improper integral if it exists

A: The solution is given as follows

Q: Use integration by parts to prove the reductionformula.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Evaluate the integral In x dx

A:

Q: Use the properties of integrals to evaluate integral 0 to 1 (4+3x2 ) dx

A: Given: I=∫014+3x2dx for evaluating given integral, first we separate terms then integrate it

Q: SSy'e»-'dy

A:

Q: evaluate the integral by reversing the orcler of integration dx oly

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Q: Evaluate the integral if it converges. Enter the exact answer, or enter na if it diverges. +00 -dx =…

A: Let I is the value of given Integral.

Q: Evaluate the indefinite integral. Show work!! dy (1-ev)?

A: Answer

Q: Evaluate the double integral: dy dr

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Q: Compute integral below with the use of substitution. eð 1 -dx x In° x

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Q: Evaluate the integral. inegral x4 /(x-1) dx

A: Given: ∫x4x-1dx

Q: Evaluate the integral s by evaluating equiv alent reversing integral obtainedd by or der af…

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Q: -dx

A:

Q: 4. f In (2x + 1) dx =

A:

Q: Find the integral. In 8x dx

A: I=∫ ln 8xx dxln 8x =t18x(8) dx = dtdxx =dt

Q: Use integration tables to find or evaluate the integral.

A: To evaluate: ∫01x1+ex2dx Evaluating the given integral, Let substitute  t=x2 dtdx=2xdt2=xdx…

Q: Evaluate the integral using integration by parts x2 In (x)dx 1

A:

Q: 2. Use reduction formula to evaluate the integral: fsins x dx.

A: Reduction formula

Q: dx -x - e

A:

Q: Use integration by parts to evaluate the integral: 15 In(s) -ds =

A: We can find the integration as below

Q: -4x + e - dx e2x

A:

Q: Solve the integral of arcsin(x) using integration by parts.

A: Given as

Q: Make a substitution to express the integrand as arational function and then evaluate the integral.…

A: Given: ∫x3x2+13dx

Q: Calculate the integral approximation Sg for 5 dx.

A: Given: ∫-105-x2dx

Q: Evaluate the integral dx using Weddle's rule. o e-1

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Q: Evaluate the integral.

A: Given: The integral, ∫12x5lnx dx.

Q: In 3 | (1- x)e"dx X In 3

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Q: Evaluate the integral. In 2 tanh x dx

A: ∫02tanhx dx=∫02sinhxcoshxdxUsing formula ∫f'(x)f(x)dx = ln|f(x)| +cHere , f(x)=sinhx , f'(x)= coshx

Q: In 2 tanh 2x dx

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Q: dx V1-x -1

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Q: Compute the given integral. Use exact values.   ∫ (upper bound = 8) (lower bound = 0) e^−3x dx =

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Q: Make a substitution to express the integrand as arational function and then evaluate the integral.…

A: To find the integral: ∫sinxcos2x-3cosxdx Let substitute t=cosx Differentiating both sides,…

Q: Use Simpson's Rule with n = 4 steps to estimate the integral. 5) dx

A:

Q: 3. x+1 dx

A: let I=∫5x32x+1dxput 2x+1=u2x=u-1x=(u-1)2and  2x+1=udifferentiate w.r.t.…

Q: Use integration by parts to evaluate the integral. | (In(3x))*dæ- 8, +C

A: The given integral is ∫(ln(3x))2dx. Let  3x=u. Differentiate both sides.    3dx=du⇒dx=13du…

Q: et * e-t Compute the convolution integral.

A:

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.