1. Evalute the improper integral 3x dx. J ' 1+ x² -1

Q: I) S dx/ (x² + 4x + 3) find integral

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Q: 1 x'Vx dx –16 x*-16

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Q: Integrate the function. S dt o. O. V6-R+ sin'1 6t + C 6t o. + C 612 o. 6t 16-12

A: We can find the integral as below.

Q: 2 y = √√√x² + 1

A:

Q: [2 0 -1 2 1] В — -1 1. Let A 3 1 [1 2 D = C = E = -1

A: DA  = 21112310-12        = 2×2+1×0  2×3-1×1  2×1+1×21×2+1×0  1×3-1×1  1×1+1×2        = 454223 (DA)'…

Q: Solve the TVP using seperation of variables By dy _x² (ity²), y(3)=0 dx

A: We solve given differential equation by method of separation of variables.

Q: Find dy/dx for x⁴+siny=x³y²

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Q: Show that d/dz(z^2 z ̅) does not exist anywhere.

A: Here we show that ddzz2z does not exist anywhere.

Q: 10. Integral 2-t dt

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Q: Use the Midpoint Rule to evaluate the integral fx-¹dx. Sx 1 O O O T N|W T 11133 113 21/3

A: Given integral is ∫12x−1dx. We have to evaluate the given integral by using midpoint rule. Here,…

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

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

Q: dy Differentiate implicitly to find dx exy 2x+9y+3

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Q: 19. Use integration tables to find J(6x +7)*/(6x +7)² +16 dx

A: