Evaluate the following definite integrals: i. ∫0  -1  (xe^(-x2+2)) dx  ii.∫1   0  (x^4+7e^x− 3) dx

Q: 3x4-4 cos x = -6

A: Find d2y/dx2 implicitly in terms of x and y3xy − 4 cos x = −6

Q: The value of (x ,y) of the following (using Gauss elimination method) 1 2 3 r2 -5r1 + r2 1 5 4…

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Q: e2x dx 10. V1+e2x

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Q: Find the indefinite integral. / (x₁ (x¹ - 9x)² (4x³ - 9) dx + C

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Q: ∫(3/2 sqrt(x )-4/x^2 ) dx ]

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Q: h(x)=5x^2 -2x^3 +1 what is h'(2)? a.-5 b.-8. c.-4 d.-8

A: The given function is

Q: find (d/dx)(3x^4+x^(1/5)/x^2-4)

A: Obtain the derivative of the function as follows.

Q: Integral of 1/18x^2-12x+34 dx

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Q: d Verify tanh - = X 1- x2 dx

A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…

Q: Prove that a quadratic function of n variables, f(x) = }xTAx + b'x +c, A e R** symmetric, be R", CE…

A: Here we are given a function of n variables as : f(x) = ½xTAx + bTx + c And we have to : Show that…

Q: If f(x)= ∫ (top 16, bottom 9) (-x^(-1/2)+5) dx. Enter your answer as an exact fraction of necessary.

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Q: Find f. Note that the coefficients and the constants must be exact values (no decimals).f^II (x) =…

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Q: Find the indefinite integral and check the result by differentiation.

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Q: Find -2 (2x5+ 3x¹) dx

A: Given that a integration and we solve this integration by using general property of integral.