Theorem If f is integrable on [a, b], then where Ar= | f(x) dx = lim Σ f(x) Δx b-a n and x₁ = a + i Ar Use the form of the definition of the integral given in the above Theorem to evaluate the integral ²₁ (4x²+x+2) dx

Q: The graph shown is f(x) = ln(x+3). 4 3 2 14 ਆਗੂਆਂ 5 4 3 2 1 1 2 3 4 5 -2- -5- +NWA U 57345 What is…

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Q: (d) | Ta2 – 4)3 dx -

A: To Determine: Convert the indefinite integral into definite integral using the interval [0,1]…

Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: 0 ㅠ 2 sin([x]) 6 [x] dx [x] is Ceiling function

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Q: Let f [0, 6] → R be the function defined as : f(x) = = -2, [4/x], if 0 < x < 1, if 1 ≤ x ≤ 6. Show…

A: Result :Every bounded function f  : [a, b] → R having atmost a finite number of discontinuities is…

Q: If m(E) = 0, show that any function f: E → Ris Lebesgue integrable and Se f = 0.

A: Given, mE=0 So, a measurable function f:E→ℝ is said to be Lebesgue integrable  (or simply inferable)…

Q: Use Theorem I to compute the shaded area in Exercise 8.

A: By using the application of integration Area  under the curve y=-x(x-3) is given byArea=∫03y dx…

Q: xdx g) 7x + 2) h)f sin(In x) dx of xe" dx

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Q: 1) Evaluate each integral by substitution: (In x) dx a)f(x+1)(x +2x)'dx b)fxVx² +9dx 「ズ dx 7x+5 dx…

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Q: evaluate the integral S ∙1 1+x²–2x³ 1-x4 dx

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Q: ¡CON(I) 1 G(r): = -T₁₂ -2 dy 1-y³

A: Gx=∫x-2cosx11-y3dy To Find: Evaluate the above definite integral Using the Fundamental Theorem of…

Q: Calculate the integral(of the picture) where f is the function f(z)=sen(z)/(z3*(z2+2z+2)). Where…

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Q: Use integration by parts to evaluate lim Sest f(1)dt. (Let u = Z→∞J f(t) and dv = est dt.)

A: As per the question we are given a limit of an integral, and we have to use the integration by parts…

Q: Evaluate the integral S de using the two-point Gaussian quadrature rule

A: For the integral I=∫abf(x)dx, the Gaussian quadrature 2-point formula is,I=b-a2w1fm1+w2fx2where…

Q: 1- sin x a) Evaluate the limit by using L’Hopital's rule lim *x→7½ 1+ cos 2x b) Evaluate the…

A: (a) Using L'Hopital's rule, take derivatives of numerator and denominator then simplify it and apply…

Q: Write down a definite integral representing the area bounded by the parabola y=x² + 4x and the line…

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Q: 3 Prove that f(x)= x² + 2x² integraliste of integrals. is on [1,1]] using definition

A: As per the question we are given a function f(x) = x3 + 2x2 And we have to prove that f(x) is…

Q: a) Find the average value of 1/x on the closed interval [1,3]. b) Evaluate the integral of2/sqrt (1…

A: see below the answer with explanation

Q: a) find the areal to the area between the grafes to f (x) = 2√x og g(x) = x^2 in the interval [0,…

A: Introduction: the concept of the definite integral is used  to calculate the area between a curves…