Example 19-36. If U, = a + bx+cx², prove that 3 U, dx = 2U2 + 12 (Uo- 2U2 + U4) 1 and hence find an approximate value for 1 exp (– x²/10) dx - 1/2

Q: 1) Use the Substitution Method to find f 12x (3x² + 4) dx . O 20(3x^2+4)^10 +C O 0.2(3x^2+4)^10 +C…

A: The given integral is 12x(3x2+4)9.

Q: S 3 (x + 1)(x² + x) -dx

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Q: d/dP (11 - 3P)

A: We have to find the differentiation of the function: d11-3PdP We know the formula of…

Q: 1 xln(x²+1) 0 x²+1 dx

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Q: S(x + 1)(2 – x)° dx 7(2 - x)* - (2 - x)* +c 7(2 - x)* -(2 – x)* +c 3. (2 - x)* +(2 – x)* +c 금(2-x)*…

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Q: Prove that (1, 2) (1,(1), 2, 3).

A: We know, if A and B are two sets then, A is subset of B  if every element in A is also in B.

Q: 12- (-11)= Express your answer as an integer.

A: Let,  D=12-(-11)

Q: S Sifoo-gool dx O d2 (f.g) = Sup {/fox) - gox|} V£₁9 € [0₂4] if d, (fig) = Find Ⓒd₁ (√x,x) @d₂…

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Q: Question 8 12x +1 dx. (2x- 1) (3x+2) Evaluate: 1 A (2x- 1) (3x+2)? %3D B) In (2x- 1)? (3x+2)| + C…

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Q: get

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Q: 28 If √1− xº + √1− yº = a³(x³ - y³) lf dy 1-y6 2 x²

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Q: 3-J (х* + 2х 3) dх

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Q: Find a general formula for dr ax + b dx" cx +d

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Q: re 1 da Ji rVI- (In x)²

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Q: its saying that D is wrong and so is fxi

A: Right endpoint method: The area under the curve f(x) on the interval [a, b], withn rectangles is…

Q: 4 Compute |w using w= - 3 - 4

A: Given a vector space V over a subfield F of the complex numbers , a norm on V is a real valued…

Q: S23% e* dx Evaluate (8e)* In8e + C (2 e)x + C In2e (2 e)X In2e + C (8e)* + C In8e

A: We have to solve the integral

Q: S(x-ae )Vx² + 2e" dx -ах - ах 11.

A: Let's find.

Q: √(x³ + 2x² + x -5) e 2X dx

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Q: 4 4 + x2 Find 3 x° + + 4/x ) dx - -

A: Given integral, ∫x3+4x+4x2+4xdx

Q: Evaluate ( ax"+5ax*+12ax*+llax²+3ax+10a x4+5z³+14x²+17x+7 dx * + 24. + In |a2 + 3x + 7| - arctan In…

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Q: d Show that In dx 1 (a) x+2 x* +3x +2 1 (b) Hence find the exact value of dx in simplest form. r*…

A: iii.a. Quotient rule of differentiation states that ddxfg=f'g-g'fg2 Chain rule of differentiation…

Q: 2x+11 1 Consider f dx = x2+x-6 x-2 x+3 then evaluate S(-dx xp(* - 3 x+3

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Q: Which of the following is/are equal to 13 dr 1+æ4 You may find the following formula useful B(m +…

A: Use improper integral

Q: Solve for t in B=Numerator x+y over the denominator t+z

A: The given equation is,

Q: valuate 2r +c + D.

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Q: 7) -U(X-2)(x+3)" (5x-1)(7x+ 2) 3х+13 6) 57 In7x+2+c) (ans.: In 5x 2х -3 7)Sー (ans.: -Im,x-1+ Im,x-2-…

A: ∫1ax+b dx =1alnax+b+C Note :As per our guidelines , we can solve first question .Please repost…

Q: In(x+1)dx 8) S x2

A: Solve the following

Q: In this section, we showed that the rule d/dx1xn2 = nxn - 1is valid for what values of n?

A: given that ddxxn=nxn-1

Q: In x dx = x* +1 now that 16

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Q: Evaluate I = | J=(1+e-x)²

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Q: az Find for z = e2z-y.

A: Given : z = e2x - y

Q: 2 19-x² 4 x² X dx

A: Solution of given question is written in below steps.

Q: Question 6 dx Using half-angle substitution, the integral is equivalent to 2+ sin x zp 1+z+z? dz…

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