3 If [E dx = In(7x - 6) - +C, find f (1). 7x - 6 Enter an integer or a fully reduced fraction such as 4, -16 , 3/7 , 1/9 etc. No Spaces please.

Q: (a) Show that y for the given z = e" In x+ xy

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Q: 10) Suppose that f is continuous and that f(z) dz = 0 and f(z) dz = 5. Find - 6f(x) dx . -3 -3 A) 30…

A: ∫-33f(z) dz = 0  ,    ∫-35 f(z) dz   = 5find -∫356f(x) dx∫abf(x) dx    = ∫acf(x) dx   +∫cb f(x)…

Q: If g(1) = -1, g(5) = 2, and | g(x) dx = -9, evaluate the integral %3D æg'(x) dx.

A: Given: g1=-1  and g(5)=2∫15g(x)=-9

Q: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

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Q: 1 (b) Evaluate the integral S ; dx 2x2-12x+26

A: To evaluate: The integral of . Formula used: Integration Formula:

Q: 32. Find the integral: dx k² +1 (-1)*2 (k² +1) а. +C 5(-1)*2*k k? +1 k+1 b. +C (-1)*2* '(k +1)(k²…

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Q: az Suppose z is a function of r and y, and csc Vr² + yz = 2"e»in z_ Solve for dz and dy

A: Given: csc x2+yz=zyesin x To find ∂z∂x and ∂z∂y.

Q: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0<t<2π)

Q: 13. Consider the integral | - dx then (which statement(s) is/are correct): x2 - 4x (i) dx : x - 4x…

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Q: The integral 2a12 + 5x° is equal to -dx 3 x5 + x3 +1 (a) -25 + C (2) +2² + 1)* (b) z10 +C (1 + کے +…

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Q: Derive a formula for In x dx where a. nt-1 b. n=-1

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Q: Find a ≤ b such that

A: ∫abx2-9dxApply the Sum Rule:…

Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

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Q: (a) Evaluate the integral ſ x e2x çdx (2x+1)²

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Q: 32. Find of In(7x² - 3x + 1). dx 14x-3 dy A. = dx C. = 7x²-3x+1 dy 1 B. = dx D. = 7x²-3x+1…

A: To find out the derivative.

Q: Find solution of an equation x X f(x) 1 1.0000 1.25 0.8000 1.50 0.6667 0.5714 1.75 2.0 0.5000 Using…

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Q: .2 -dædy In (x) ey

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Q: 1. Evaluate these: 1 -x* +c dx *dx (i) x'd< (Ans. x² +c J; (iii) |xdx dx (Ans. ); (ii) (Ans. 2 5 );…

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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: 4. Find the Cauchy principal values of the following integral: dx. (x²+1)(x²+2x+2)

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Q: 1. What should be A for the path independent of (2,4) 2Ay – x -dy. y? xy + A - (1,2) Moreover…

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Q: An object is moving along a path defined by the graph   x2+y2=2   Compute dy/dy, if dx/dt=2,x=−1,…

A: Differentiation application

Q: хах 11. The integral f 4-х2 is equal to 1 A. In | | + C C.-글m14- x리 + C 4 x+2 2+x B. In |4 – x2|+C…

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Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

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Q: 2. Find the integral 2x+3 dx x2-9 a. In/(x – 3)³(x + 3) + C а. b. In[(x – 3)³(x + 3)] +C c. 2ln[(x –…

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Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: If g(x) = - - S^*[e'- In(2t+1)]dt, find g'(x) . dx A ex-In(2x+1) 4 B

A: We can solve this as follows:

Q: 3+ Evaluate the integral: Se³+ cosh2x33+ cosh2xsinh2x dx (3e)³ 3+ sinh2x A + C 21n3 (3e)3 + sinh2x B…

A: Application of integration

Q: 5. Test the ff ODE for exactness and find the general solution of the DE (2x + 3y) dx + (3x + 4y)…

A: To solve Differential equation.

Q: 18 2 6x dx using n = 2, 4, and 8 subintervals 2

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Q: Evaluate the following integral. dx (x² + 16)2 (A) 능 (구16+ 16arctan()) +C (B)(+16 +is arctan() + C…

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Q: 4 2 Compute f S 4xy dy dx. 1 0

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Q: dx Evaluate the integral: (+3x-7) A ++ In|3x-6|+C 5 +5x+! In/x-21 +C B 3 с +5x+31n|x-2|+C D x² + 5x…

A: You must have idea about logarithmic properties to simplify this expression. Understanding of…

Q: d ** If g(x) = [e² – In(2t + 1)]at , find g" (x) dx A ex- In(2x + 1) 4 ex - (2x + 1)2 B (c) none of…

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Q: S x2 +2x-10 (2x+4) + 1 JE + 4x +5) Consider dx = x² (x² + 4x + 5) (2x+4) + 1 dx- x² + 4x +5 dx ,…

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Q: 1. Evaluate the definite integral S ,2 C (9x² + 5)dx by the limit definition.

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Q: 6. Suppose f(2) is analytic in |2| 1, and f(0) = 1, f(0) = 2, compute: %3D (1) h = fe(s+ 1)2d: (2)…

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Q: In 3-Jın Evaluate the following: dx 2e*cose*dx T/3 4 sinx dx 1-4COSX 2-Jo x(lnx)² 1- Jo" x(Inx)?…

A: Given that three different types integration we solve these integration by using general formulas of…

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

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Q: If x = k (1+ e*) dy _ x² + x°ew/ s° +2yeb/a} prove that dx 2xyely/x}

A: NOTE: Refresh your page if you can't see any equations. . ................(1)

Q: ** If g(x) = S [e* - In(2t + 1)]at , find g"(x) dx ex. (2x + 1)2 A ex – In(2x + 1) 4 ex + (2x + 1)2…

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Q: メ1+ x€ Lat F Cx, x = F•dr whera yer CIS elosed c is Sagmants from C0,3) to Co,0) than from C3,0) to…

A: Given F=yexyi +xexyjand path is closed

Q: 8. The value of the integral 2[x] 1o sulsV ar 3x-[x] dx, where [] denotes the greatest integer 2[x]…

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

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

Q: -X +7 Evaluate the integral: dx (x-2)(x+3) In x - 2|+2 1n x +3 +C 2 In |x – 2| – 2 In |x + 3|+C 2…

A: First of all we will do partial fraction, then we will evaluate the integral.

Q: If g(x) = — _*[e'-in(21+1)]dt, find g''(x) . - dx 2 A ex_ (2x + 1)2 B e* - In (2x + 1) 4 с ett (2x +…

A: Given:  g(x)=ddx∫-2xet-ln(2t+1)dt To Find: g"(x) Formula to be used: Fundamental theorem of…

Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…

A: Solve the integral  √(x2+25)/9x2

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

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Q: Prove that by Gamma Function pit +e e-st dt %3D s2 +1

A: Gamma Function: The gamma function, denoted by is denoted by which is convergent for Some…