Consider the area between the graphs x + 4y = 5 and x +7= y'. This area can be computed in two different ways using integrals

Q: / 1 – x2 dx (c)

A: Given I = ∫1-x2x3dx    ......... (1) Integration by parts ∫u(x).v(x)dx = u(x)∫v(x)dx…

Q: Evaluate the integral using by parts method: S 6x5 In 3x dx

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Q: By using double integrals find the area between x = – y², lines y = x – 4, y = -2 and y = 2.

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Q: The value of the integral Vx dx computed using Trapezoidal rule with 2 subintervals is (Rounded upto…

A: The trapezoidal rule uses the area of the trapezoids to approximate an integral. Using the…

Q: evaluate the incdesinite integral -5x+3)dx

A: See the details solution below

Q: Evaluate the integrals using integration by parts. ∫x ln x dx

A: Here given integral as Use the formula of integration by parts which states

Q: Evaluate the integrals using integration by parts. ∫ (x + 1)2ex dx

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Q: x sec (3x) tan (3x)dx

A: We use integrate by parts to solve the given integral.

Q: Evaluate the integrals using integration by parts. ∫e2x cos 3x dx

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Q: Evaluate the integral using tabular integration by parts. 7 x V2 x + 1 dx

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Q: Evaluate the integrals using integration by parts. ∫ ln (x + 1) dx

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Q: Evaluate the integrals using integration by parts. ∫xe3x dx

A: Concept: An integral is either numerical value equal to the area under the graph of a function for…

Q: S 8-3x (x+1)(x² − 4x+6) - dx

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Q: 10x Selar. 20x dx 1- °

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Q: Find the approximate value of integral from 0 to 10 1/√(x2+1)dx to 4 decimal places using Simpsons…

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Q: Evaluate the integrals using integration by parts. ∫(x2 - 5x)ex dx

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Q: Evaluate the integrals by using a substitution priorto integration by parts. ∫ln (x + x2) dx

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Q: Use any method to evaluate the integrals ∫ ln x + 2/x (ln x + 1)(ln x + 3) dx

A: To evaluate the integral ∫lnx+2xlnx+1lnx+3dx, first use the sum rule and separate the integral as…

Q: Evaluate the integral using by parts method: S9z In 4x dx

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Find the area of the loop of the curve y2=x3 (1-x)6. Show complete solution of points of…

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Q: When we find the area between an upper curve f(x) and a lower curve g(x), we integrate f(x)-g(x).…

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Q: 2. +4) dx

A: Given: ∫02x2+4dx

Q: Evaluate the integrals using the substitution method of e8x dx

A: To evaluate the integral: ∫e8xdx Solution: Let substitute t=8x. Differentiating both sides, we get…

Q: Evaluate the integrals using integration by parts. ∫x3 ln x dx

A: the given integral is: ∫x3lnx dx we have to evaluate the integral using integration by parts. lnx is…

Q: Evaluate the integrals using integration by parts. ∫ ex cos 2x dx

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Q: Evaluate the integrals using integration by parts. ∫x2e-x dx

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Q: Use the method of anti-derivative to find the area under the curve y = 4(x³ the interval [2,4]. 4x)…

A: Before finding the area, first, we will find the x-intercepts of the curve  to check that any point…

Q: Evaluate the integrals by using a substitution priorto integration by parts. ∫x tan2 x dx

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Evaluate the integral using integration by parts where possible. x In(8x)dx

A: Given: ∫12 x ln(8x) dx To find: Value of the integral.

Q: Evaluate the integrals using integration by parts. ∫p4e-p dp

A: ∫p4e-p dp

Q: Evaluate the definity integral  from 0-4 (x-3)(x-5)dx

A: Evaluate the integral ∫04x-3x-5 dx.

Q: Evaluate the integrals by using a substitution priorto integration by parts. ∫sin (ln x) dx

A: Given: I=∫sinlnxdx for evaluating given integral, we substitute lnx=t…

Q: Determine the indefinite integral of ſ Vx6 + 3x5 + 3x4 + x³ dx

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Q: Find the area under the loop of the curve y2=x4(x+4) using integration

A: An integration formula for calculating the area under the curve will be used. We will calculate the…

Q: Evaluate indefinite integral: dx / (x+3) * squareroot of x2+6x

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Q: Evaluate the double integral that will solve for the area of the region bounded by y = cos(x) + 5, y…

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Q: Calculate the integral approximations Ts and Ms for L'(In x)-2 dx. Your answers must be accurate to…

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Q: Solve using iterated integrals. (with graph) Find the smaller area cut from the circle x2 +y2 = 25…

A: The objective is to find the smaller area cut from the circle x2 +y2 = 25 and x=3.

Q: Use the general power rule for integration to find the indefinite integral. a)∫10x/(√5x2+13) dx…

A: a) The general power rule of integration is of the form ∫fxnf'xdx=fxn+1n+1+c   Let fx=5x2+13. So…

Q: Use any method to evaluate the integrals ∫ x4 - 1/x5 - 5x + 1 dx

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Q: Solve using iterated integrals. (with graph) Find the area bounded by x2-6x+y=0 and x2-2x-y= 0

A: The objective is to find the area bounded by x2-6x+y=0 and  x2-2x-y=0.

Q: 5. Find the area under the curve integrate 2/(9 - x ^ 2) dx

A: Given;           ∫29-x2 dx Take the constant out: ∫a.fx dx=a.∫fx dx           =2.∫19-x2 dx Apply…

Q: 2-V1-x dx by interpreting the integral in terms of area. -

A: ∫-112-1-x2 dx On simplification, we get ∫-112-1-x2 dx=∫-112 dx-∫-111-x2 dx   →1 Now consider, ∫-112…

Q: Evaluate the integrals using integration by parts. ∫(x2 - 2x + 1)e2x dx

A: To evaluate ∫x2-2x+1e2xdx

Q: Use Property 8 of integrals to estimate the value of the integral. ∫20(x3-3x+3)dx.

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Q: 4) Reverse the order of integration in 2 2x x' dydx 0 x2 and evaluate the integral as an x-simple…

A: To reverse the order of the below integration. ∫02∫x22xx3dydx

Q: ) dx

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Q: Evaluate the integral by reversing the order of integration. 12 3y Ар хр

A: Solution is given below :

Q: Evaluate the integrals using integration by parts. ∫ x2 ln x dx

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Q: 15. Ssin (In x) dx.

A: If  u and v are function of x then the integration of uv by parts is given by…