(x.y) on the curve r(t) = (2t",7t), for 1sts2 F = (x² +y?) 312 The value of the line integral of F over C is e an exact answer, using cadicais as needed.)

Q: suppose A is a positive real number, determine the area of the traingle enclosed by the lines x=0,…

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Q: Ss (2ava2 + 2) dæ dx r+1 vi) đt 64 Jo (sin 2x + cos 2x) dz

A: Firstly let's recall few basic integration formule.

Q: Given the velocity function v of an object moving along a line, explain how definite integrals can…

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Q: 9) Find the equation of the tangent to the curve y = 1+ Int and x=t+Int when t = 2.

A: Given problem:- Find the equation of the tangent to the curve y = 1 + lnt and x=t+Int when t = 2 .

Q: Q4 Find the integrals of the functions. (Answer Five only ) 3- )tan t sec?t dt dx 4- S: xV5x2-4

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Q: Evaluate the integral f [[ - Y sin(x²)dxdy.

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Q: . +2 sec? (20 - ㅠ)) dθ 20- ㅠ

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Q: ·2² cos(32)dz where C It's the curve 4x2 +9y? = 36

A: Cauchy - Gaursat theorem is used to find integration

Q: d Compute [(* + 2x)} ] a x= -1. dx

A: ddxx5+2x2=2x5+2x5x4+2

Q: The table below shows speedometer readings at 10-minute intervals during a 30-minute period of the…

A: The right rectangle approximation method takes the rectangles formed by the values of the function…

Q: 1. This problem is about linear independence and dependence. Let S= {₁, 2, 3) be a subset of R¹. (a)…

A: A vector  is written as  where . For example: is a vector belonging to .It is given that  is a…

Q: Evaluate following integral using one-dimensional Gaussian Quadrature. Compare results using 1 and 2…

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Q: b) sec* 0 d0 Give the exact answer.

A: The given integral is ∫π4π3sec4θ dθ

Q: 3- Find the value of integral by using the Gauss quadrature (three points) I = -dx x+1

A: We can find the approximation of the integral of a function over a closed interval  usingthe Gauss…

Q: f(z* - y)dz – 2rdy where C It's the curve x? + y? = 4

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Q: í e (ex + 1)? dx А. х В. еx C. (ex +1)2 D. ex + 1

A: using integration by substitution

Q: Q) Find the relation error use the Simpson's rule to approximate the definite integral. Use n=4,5xdx…

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Q: (x² + y²)dx + 2xydy where C It's the curve y = x³ from x = 0 to x = 1

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Q: Use u-substitution to compute integral for question G2 please.

A: Factor out sqrt(x) from the denominator:

Q: de Use contour integration to evaluate the real definite integral 17- 8сos(®

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Q: V3 4x dx 15. Evaluate the definite integral -3 x2+1 (Hint: determine if F is odd or even)

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Q: Using the residue theorem find integral of the function (z + 1)/(z + 2z) with respect to z within…

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