2 dt Ji P(t + 1)

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Q: Integration Evaluate the following integrals.

A: To evaluate the given definite integral.

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A: Consider the given integral is Simplify the integral

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A: We first try to write the numerator using (x-1) and (x+2)

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A:

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A:

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A: ∫x2x+2dx Now put x+2=t⇒1+0=dtdx⇒dx=dt

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A: The given integral is ∫21x2x3-x2-12xdx. Note that…

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A: ∫11+cos4θdθ

Q: Integration techniques Use the methods introduced evaluate the following integrals.

A: The given integral is ∫x2+4x+7x+32dx. Let x2+4x+7x+32=Ax+3+Bx+32+Cx+33. Remove the fractions and…

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A:

Q: TRANSFER TRAN SFER ACTIVITY 2: INTEGRATION THROUGH SUBSTITUTION Direction: Evaluate the following…

A:

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A: The given integral is ∫π4π2xcsc2xdx.

Q: Integration techniques Use the methods introduced evaluate the following integrals. ∫x2 cosh x dx

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A:

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A:

Q: Integration Evaluate the following integrals.

A: Given        ∫x3-10x2+27xx2-10x+25dx

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A: The integral is given by ∫x6+2x4+x2+1x2+12dx By long division,…

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A:

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A: To evaluate ∫x3+5xx2+32dx

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A:

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A: We need to evaluate the integral using integration by parts.

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A: The given integral is ∫x2+x+2x+1x2+1dx

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A: Given ∫6x2x4-5x2+4dxWe need to evaluate the above integral.

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A:

Q: Integration Evaluate the following integrals.

A:

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A: To evaluate the integral: ∫x2-4x3-2x2+xdx. Simplifying the expression.…

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A: The given integral is ∫t-12t dt. Let x2=t-1. This gives t=1+x2   and  dt=2x dx. Substitute these…

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A: Given:∫dxx2-x-2

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A: To evaluare the integral: ∫t3-2t+1dt Given integrand can be written as: t3-2t+1=t2-t+1-3t+1 Now,…

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A: To solve the integral,  ∫dxx3-2x2 Factor out x2 from x3-2x2, x3-2x2=x2x-2 ∫dxx3-2x2=∫dxx2(x-2)

Q: Integration Evaluate the following integrals.

A: Let the given integral be y - y = ∫2z3+z2-6z+7z2+z-6dz           ................(1)Let,f(z) =…

Q: Integration techniques Use the methods introduced evaluate the following integrals.

A: Given: ∫03249+4x2dx

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A:

Q: Integration Evaluate the following integrals.

A: Given integral, ∫9x2+x+213x2+72dxwe have to evaluate the given integral

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A:

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A: Given: ∫6x3 -4x+1 dx To evaluate: The given integral and check it by differentiation.

Q: Integration Evaluate the following integrals.

A: To evaluate integral I = ∫x3 + 2x3-2x2+x dx I = ∫x3 + 2x (x2-2x+1) dx I = ∫x3 + 2x (x-1)2 dx

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A: Given  To evaluate

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A: we have to evaluate the given integral  ∫8(x2+4)x(x2+8)dx

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Q: Integration Evaluate the following integrals.

A: Given: An integral ∫8x-53x2-5x+2dx Firstly, write 8x-5 as 436x-5+53 and split.…

Q: Integration Evaluate the following integrals.

A: We divide 3x2+4x-6 by x2-3x+2 using long division. x2-3x+233x2+4x-6                    3x2-9x+6…

Q: Integration techniques Use the methods introduced evaluate the following integrals.

A: Given integral is I=∫3xx+4dx We will use the substitution method to solve the given integral. Let…