1.5 If In x dx = 1 and " In x dx =1+ e?, then Inx dx =: a. b. In 2 C. d. e2 е. 1+ e?

Q: d In (t2 + 1) dt = dx A) In(x6 + 1) B 3a In (a? + 1) 3x ln (a6 + 1) In (x® + 1) In (e? D -

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Q: L{t + et} =+ I. L{t + e3t} = = 1 %3D II. S-3 52 5-3 L{t + e*} =+ L{t + e#} = - III. IV. S+3 52 543

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Q: 22. How large should n be to guarantee that the Simpson's Rule approximation to e dx is accurate to…

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Q: Use Simpson's Rule to evaluate the following. n = 10 +3 1 dx J-3 1+x²

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Q: 59. Show that for any number a > 1 -Ina In x dx + e dy = a In a,

A: Given: ∫1alnxdx+∫0lnaeydy=alna

Q: 1. Find the following antiderivatives. (a) [² cosh x + 1 sinhx dx

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Q: 5 (2) (-2%) e dx %3D

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Q: 1. Approximate dx using each of the following.

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Q: 43. (In z)² dx

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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: If f(x) = exp(-x).In(x), then , when x=1, df/dx is 1/e C 2/e O e nonexistent O

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 1) Find the following integals: 14) S(2? -x) dx le) S x* dx la) S x* dx Ic) )치 dr If) Sdx ax ti

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Q: 뿐 for the following: y = ln(e2z) 0 읊 ○ 2 Oezz ○ ez (In 2)

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Q: If In = + a?)" dx, show that - (x(x² + a²)" + 21na²In 1]. 2n + 1 1 In

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Q: If f(x, y) = e®¤ . In(16y), then fræ is given by: O 144 e9 In(16y) O - 81 e9 ln(16y) O 81 e9 In(16y)…

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Q: The integral 2n / 14xe dx can be done with the substitution u - and du= dx.

A: Step 3Given,2π∫14xe-x2dx

Q: 2x e3a² dx

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Q: calculate SN given by Simpson’s Rule for the value of N indicated.

A: Width of each interval= (4-1)/8= 3/8=0.375 So, the partition is: 1, 1.375 , 1.75, 2.125, 2.5, 2.875,…

Q: The approximate value of [(e^² + 4x² − 8) dx by a single application of Simpson’s 3/8 rule išº − is…

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Q: Calculate SN given by Simpson’s Rule for the value of N indicated.

A: In this Rule, N is an even number and h = (b – a) / N. The y values are the function estimated at…

Q: evaluate the following intergertal     (e−x + 2x)2 dx

A: Given integral is By using the identity (a+b)^2=a^2+b^2+2ab, we get

Q: 20. In(e**) = e2iny A. = - D. = dy В. dx dy dy С. dx dx у dx

A: Given equation is ln(ex^(2))=e2lny

Q: S 8x dx/1+4x? (x = 0 to 1/2) * O In (2) In (6) O In (4) If y = (x? - 1)/(x² + 1) then dy/dx 2x / (x2…

A: Q-1 : I=∫01/28x1+4x2dx =∫01/2ddx(1+4x2)1+4x2dx (∫f'(x)f(x)dx=lnf(x)) =[ln(1+4x2)]01/2…

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

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Q: How large should n be to guarantee that the Simpson's Rule approximation to dx is accurate to within…

A: Given:  ∫017ex2dx             where f(x)=7ex2 and a=0 , b=1.

Q: 1 dx x(In x)*

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Q: Which of the following is represents an estimate of 2 o e*dx using rectangles with heights given by…

A: We have to find approximate value of given Integral using right sum.

Q: S°1- (In x)2 dx=? If u= In x, then e A B L (1- u)du .2 © (1-u²)du

A: Given: I=∫ee21-lnx2xdx   ....1

Q: Apply the open Newton-Cotes formula with 3.5 xe*dx n=1 to approximate 0.5

A: For n =1 , ∆x = b-a3 , and the abscissas are x0 = a+∆x and x1 = a+2∆x . The Lagrange polynomials…

Q: calculate SN given by Simpson’s Rule for the value of N indicated.

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Q: L{e¬at cosh bt} = %3D

A: The given function is e-a tcosh bt. The main objective is to evaluate the value of Le-at cosh bt.…

Q: (e) /a (с) dx e2x 2.х

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Q: 1 dx Jo 1+x3 O 3/26 (In 8 + nv3) O 1/10 (In 8 + 2t) O 1/9 (In 8 + v3) O 2/19 (In 8 + 2n)

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Q: Evaluate e dx 3 2 + C O x + C O 2/x + C In e + C

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Q: حالة إكمال الأسئلة السؤال 5 In dx= .a O .c O .d O 346I JS Kásl "übbUI JS báa" ġgå jäilg - Jluujllg…

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Q: Choose the letter of the correct answe. 1) x² (xdy + ydx) = (5- xy) dx a) x ln (5-xy) = 1- cx b) -x…

A: We are allow to solve first question only .If you need rest of answer please upload it separately…

Q: Evaluate SSS 12z dV E where E is enclosed by z = x? + y? and z = 1

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Q: dy y(ln y- In a+1) dx 1 C = -In 1 C = In O Option 2 Option 1 1 C =-In None of the choices O Option 4

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Q: Solve the folkowing di fferential equotions 1. xdy dx + dy x'

A: Firstly , we can solve for dydx. After that we can see that the equation is an homogeneous…

Q: In 4 In 5 e2X+ Ydy dx = 0 1 (Type an exact answer)

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Q: (e 2x -1)2 dx 1. e 2x

A: A detailed solution is given below

Q: In n (4) {} (e) {E 5Vn + Vn J

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Q: S 3* e*dx

A: Integration means addition it is used for adding continuous function which can't be added by simple…

Q: - Find the value of the following integral: 1) fe et -e" dt e~st 0. 2) e-tdt 0.

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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: 1.) Evaluate In 2 e*2arctan e* A.) Jū+e2x) sec(2ªrctan e*) dx

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

A: The given integral is divergent.

Q: 12. Verify that the t ratio for testing Ho: B1 =0 is identical to t for testing Ho: p= (0.

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Q: s) sohne rec'x pecy dx + sing dy = 2

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Q: Q1 Evaluate the following: Ine dx n/3 4 sinx 1- Jo 2- Jo x(Inx)2 3-m 2e*cose*dx in 1-4cosx

A: Simple integration problem.....