(a) Use n = 6 subdivisions to approximate the value of Vx + 3 dx by the trapezoidal rule.

Q: A drone flies with velocity v(t) = 3ti-fj+4k. When t = 1, the drone is at (3,2,2).

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Q: (I+x²)d (l-x²) Vi+

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Q: c) Evaluate [| 4xy where D is the portion of x + y = 2 in the 1* quadrant.

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Q: 4 sin-lx dx X.

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Q: x2+1 - dx x4-x²+1

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Q: dx Vx + a + Vx + b

A: Given: The integral is ∫xx+a+x+bdx

Q: | (3 + xx) dx

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Q: Arctan°9x dx =b Arctan 3x+C, i+9x2 what is b?

A: Solving the given integral by substitution.

Q: Show that (xcos(2x)dx=. A-2 8

A: LetI=∫0π4xcos2xdxPut 2x=udifferentiate on both side2dx=dudx=du2As x→0 then u→0As x→π4 then…

Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: (c) Evaluate (1+ Væ)' S dx. 2C

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Q: Use geometry to evaluate (2x + 6) dx. -5

A: We know definite integral   ∫abfxdx represent the algebric sum of the areas between x=a to b and…

Q: Find dy. y = 33 + 10x4 – 5x5 dy = (Simplify your answer.)

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Q: Compute 3+r+1 dx x2

A: Given : ∫233x2+2x+1x2dx

Q: Show that: -1 xb-1 In x dx b2 2-

A: we use integration by parts

Q: Use n = 6 subdivisions to approximate the value of Vx +2 dx by the trapezoidal rule.

A: The given integral is ∫06x+2dx and the value of n is 6. Using the trapezoidal rule, approximate the…

Q: A = - 1)³² dx - (x - 1)³dx + 5²0x

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Q: (1 +Iпx) dx x3

A: The given integral is ∫1+ln xx3dx. Here, u=1+ln x  and  v=1x3.

Q: Evaluate ſ²¹₁ (y +1) (y² + 2y)³ dy. Give your answer correct to 2 decimal places.

A: The given equation is, We have to solve this definite integral to get an answer in 2 decimal…

Q: 1 dx 4+vx 10.

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Q: dy Find if dx y = (3x2 + 6x – vx)(5x + + 10). DO NOT SIMPLIFY.

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Q: Q.2: Evaluate: -2 2 dx 1 I = x2 - 8.

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Q: Find dy for y = (4x +2)2. dy = (Simplify your answer.)

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Q: V3 3 9) 9 +x2

A: The given integral,        ∫0339+x2dx