If Ux = a + bx + cx², prove that S²³U¸dx = 2U₂ + 1⁄2 (U₁− 2U₂ + U4) and hence find an approximate value for 2 P exp (-x²/10) dx

Q: 0.2+ 25x+ 3x2) dx

A: Simpson's 13 rule: ∫abydx=h3(y0+4(y1+y3+y5+...++yn-1)+2(y2+y4+y6+...+yn-2)+yn), where h=b-aN and N…

Q: 7. Find 3 So 1 X x5/2 + x3/2 -dx

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Q: 77. Use substitution with u = x² + 4x + 3, = (x +2) dx.

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Q: Show that

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Q: X x²dx 5+ x2

A: Find the integral

Q: sin 5 (17x) dx = [

A: To evaluate : ∫sin517xdx Let I = ∫sin517xdx ⇒I =∫sin417xsin(17x) dx

Q: Evaluate B f da where A = (x² - 1) and B = 22. You must show all steps.

A: Given data

Q: / In (x? – x + 2) dx — х+2) dx

A:

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: Integrate 1. S the following: (x²-3x²) dx (x4-4x3+2)3 3 √x-2 z² 2 2. S dx 3. S dz 4 √73-2 3.

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Q: Show that S, (In x)? dx = e – 2

A: The detailed solution is as follows below:

Q: 3x2[x18 + x15 sinh(ax³)] dx

A: Given that ∫3x2x18+x15sinh(ax3)dx, 3∫3x2x15sinh(ax3)+x18dx Take u=x3→dudx=3x2,…

Q: e3 sin(5x) dx %3D

A:

Q: xx (x)dx X 3TT 28

A:

Q: In(ere + 12) dx Xet

A: Given : ∫x2ex2lnex2+ 12dx

Q: 2. (a) Evaluate [ x* V1+4x² dx. (b) Evaluate 8x° +13x dx. (x² +2)²

A: (a) We have to evaluate the following integral: ∫01x21+4x2dx Then we get,…

Q: Calculate dy/dx. You need not expand your answer. y =x2.3/9+2/x2.3)(9x − 1) Answer ----->dy/dx:…

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Q: ۱۴ 14 g 3 3+1x 1= x² + 1× AND -FIND /dx WHEN X=2 =6.

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Q: 1 dx J 2/3 (1+ x/3)

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Q: Solve cosh(z)=1/2

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Q: Sx² cosh (1-x³) dx

A: Let the given integral be I - I = ∫x2cosh1-x3dx                   ............(1)Let,t = 1-x3…

Q: Evaluate : e2x sin3x dx

A: Introduction :

Q: (x³+3x) dx x3+1

A:

Q: Evaluate 1 dx (x - 2)³

A: we have to solve the integration

Q: 3. Solve the following: 2xdx (x²+1)2 a. b. y = f xe* dx, given y=0 when x=0 x-2x+1 dx с. d. sn (Inx)…

A: According to our guidelines we can answer only first three sub-parts and rest can be reposted.

Q: If In = f(In x)" dx, show that In = x(lnx)" - nln-1. Hence find f(In x)³ dx.

A: Given that In=∫ln xndx, we have to show that In=xln xn-nIn-1 and also find the value of ∫ln x3dx.

Q: 1 2. dx (e2x – 4)*/2

A: