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: 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: ¡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: 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