Evaluate: ³4²₁²[z³(x + y)³] dz dy dx

Q: x³ dx 9+x* 1.

A:

Q: Find ∫√(2x − 1) dx.

A: Given:

Q: (x*y - 2xy) dy dx 2.

A:

Q: (I+x²)d (l-x²) Vi+

A:

Q: 7. Use substitution to evaluate ſ 2x(4 – x²) dx.

A:

Q: x2+1 - dx x4-x²+1

A:

Q: Evaluate the to -y dxd

A: Given that, the integral is ∫01∫01-y2x2+y2dxdy. Obtain the value of ∫01-y2x2+y2dx.…

Q: (x²y – 2ry) dy dx

A:

Q: .2 dx Jo (9 + x²)2

A:

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: Find if y = (x² – 1) (x³ + 2). dx

A: We expand the given expression and then use power rule to find the derivative.

Q: (1 +Iпx) dx x3

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

Q: Find So S 4:xy dx dy.

A: Evaluate the integral.

Q: Evaluate x(x2 + 1)3 dx.

A: Given ∫x(x2+1)3dx

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: Evaluate: 2 (+8xy) dy dx

A:

Q: Calculate the following integrals a) S .3 dx;u = x³ – 1 | Vx3-1 3x b) S dx; u = e3x +1 e3x +1 c) S *…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1 dx x(x²+4)?

A: Answer

Q: (4 – y²) dy dx 0Jo

A: Using double integration.