Using Beta function, show that dx 3- (b – x) (x – a) |

Q: 5. S sec(3x) tan(3x) dx

A: formula:∫ secx tanx dx =sec x +Cwe are given;I=∫ sec(3x) tan(3x) dx3x =t3 dx =dtdx =dt3

Q: dy for all of: dx Find 3 x(x-2) 2- у %3 x2+1

A: We will use simple differentiation rules to solve this question.

Q: tionship between x and y.

A: Linear Eq: 9.x=1,2,3,4,5y=f(x)=2,4,6,8,102y=xSo, this is the requiredequation of line.

Q: dx x Vx²+2x-1

A: In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or…

Q: (sinx E,x# 0 a) f(x) = in x = 0 0, x = 0 b) f(x) = x - |x| in x= 0

A: Topic:- Continuity

Q: Using Boole's Rule, Evaluate (x² + 3y²)dxdy

A: Given:                ∫02∫0yx2+3y2dxdy To do: Evaluate the integral using Boole's rule.

Q: Evaluate integration 1/(x^2-9)^(3/2) dx using trigonometry substitution

A: Consider the given integral as ∫1x2-932dx. We use the trigonometric substitution x=3sect to evaluate…

Q: Find dy/dx by implicit differentiation. 6) x3 + 3x2y + y3 = 8 dy A) dx x2 + 3xy B) dy dx x2 + 3xy x2…

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Q: xsin x -dx, a > 0. x +a 15. Evaluate by method of residues |

A: Residue theorem

Q: Integration

A: We will solve the integral.

Q: integral tan3(x)sex(x)dx

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Q: ) Isinx-sinyls lx-y!

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Q: integral (dx/(√(x)+x))

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Q: Function dy du dy du dx dx = (5x³ – 7x² + 2x – 3)*) _y = csc(x² – 3) y = 5x² – . y = V5x2 – 4 _y =…

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Q: | sin“ x cos' x dx 4. Integrate:

A: Given: ∫sin14x cos5x dx  To find: Value of the integral.

Q: arctan(x) dx = x arctan(x) - 2 In(1+ x?) + c

A:

Q: integral Scos 4 (3x) Sin (3x) dx Evaluate the

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Q: Implicit differentiation Ex. Find dy/dx: x² +xy+ y = 5

A: We can find the required implicit derivative as below

Q: x +1 -dx x² (x – 1) (a) Integrate

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Q: Can i get help step by step please

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Q: arctan(x) Evaluate dx or show that it diverges. 0, x² + 1

A: Using the fact that, 1/(1+x^2) is the derivative of arctan(x).

Q: Limit -1 to 1 integral (1-1/2 x) dx

A: Given:        ∫-111 - 12x dx   To find the value of ∫-111 - 12x dx   Formula:          ∫xn dx = xn…

Q: te technique ∫dx/x^2

A: In general, the integral of a real valued function f(x) with respect to a real variable x on an…

Q: tanx -√ S sec²x 1+ et tanx In (secx) √✓ 1+tan²x 1+ elanx sec ³x 1+etanx If f(x) = A B (с 1+1² 1+e'…

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Q: Using the Chain Rule Find dy/dx for y = (x2 + 1)3

A: Given, y=x2+13 We can write given function as, y=x2+12x2+1 Now by using the chain rule,

Q: antiderivate of y = sin x + 6x2

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Q: CNIVERSI Find if f(x,y) = y sin xy 3.

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Mic differentiation to Find der :Vative Of Y «in(x+7) x+7)* (In(x+7) + X. X-1 H7)* (x+7) t x+7

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Q: ly Exercise: Find dx 1. y. 10x+3 Cosx y lox +3 Cosx +子 Cotx 3) 14 Cotx

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: (b) YOUR TURN 4 Find dx. Vx f(x) deriv for in

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Q: Cos ly -A) %3D show that 2 ニ0 2 8x Sx8y

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Q: ropriate integrating factor after transforming it into linear u wstitution of 2

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Q: 2)8 Sx' 1- x dx

A: Indefinite integration

Q: sin x In x Differentiate the function: Y =e

A: The given function is y=esinxln x. Product Rule: ddx(f(x)·g(x))=f'(x)·g(x)+g'(x)·f(x) Chain Rule:…

Q: ·sec-x)" sec'x 23. What should be the value of A for -dx to be integrable using the formula | u" du?…

A: the integration of the integral is (2-sec2x) eln(pi/e)sec3x/Sec(3A-x).

Q: Estimate - dx using left endpoints for n = 3 approximating rectangles. х 2 dx is approximately

A: We have to find the Riemann sum for ∫232xdx with n=3 rectangles, using left endpoints.

Q: dy for all of : dx Find 3 x(x-2) 2- y = V x2+1

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Q: dx |x3 +1

A: Solution

Q: i) Integrate  f sin 3x dx                                                                       ii)…

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Q: sech x+csch x Q3: prove that e2x %3D csch x-sech x

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Q: Using Monte Carlo, estimate the value of eTy dx dy.

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Q: arctan x dx (けx) It X

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Q: 2 What is /- dx? oJ-dx = -sin-x+ C %3D /I-x² • /-dx = 2sinx+ C %3D dx = -2cos-x+ C %3D oS- dx =…

A: We will solve the given integral.Below find the solution in image.

Q: ppose f(x)= -cosx-4). Evaluate dx

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Q: 3- Using Beta function, show that dx = Tt (b – x) (x – a)

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Q: 5-7 -1 Using quotient rule, show-that d [cotx] dx 2. 1+x

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Q: [sin x cos“ x dx 14 4. Integrate:

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Q: dy 1- Find by implicit differentiation. 2- x2 + y2 = 100. 3- x³ + y³ = 3xy². 4- x²y + 3xy³ – x = 3.…

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Q: Partial Differentiation a2z 1. If z = e* sin y + e³ cos x, verify a²z = 0 ду?

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Q: Beta Function 27 dx (*+ 1) Prove that

A: The given problem is to evaluate the given beta function integral.