6. Evaluate 1 x² + y² + x² dV, where E = { (®,g, z) |1< n? +g? +z? <4}.

Q: Evaluate 3 | ((2 – 1)32, (3 + t)2, 1)dx. 3/2 3/2 -3

A:

Q: 7. Find 3 So 1 X x5/2 + x3/2 -dx

A:

Q: 1 dx = x(x* + 1) Select one:

A:

Q: Evaluode Lim [x]+[2x ]+ n2

A: We know that, x-1&lt;x≤x Therefore, 2x-1&lt;2x≤2x ⇒3x-1&lt;3x≤3x . . . ⇒nx-1&lt;nx≤nx ∴ (x + 2x + 3x…

Q: What is the value of k if any So kxe* dx = 1

A: This question is taken from the Definite integral in which we have to find the k value by solving…

Q: Q3. Evaluate f: 2*+1-5x-1 dx 10

A:

Q: Find √√3 x² +3 x² +1 dx

A:

Q: 2.1 Evaluate f xvx +5dx (10 marks)

A: Given that   xx+5 dx Substitute u=x+5 →dudx=1  and x=u-5 ∫xx+5 dx=∫u-5 u du…

Q: 1 Evaluate : dx. (1+x)Vx -x X-X

A:

Q: Differentiate. Find ele ele ele ele ele AP O AP O for y=x-1 Whatsa AP O 2x³ - 3x² (x −12 - 2x3+3x2…

A:

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

A: See the attachment

Q: If y = ((5z² + 8z)³ – 5-)°, then dy/dr is:

A:

Q: 3/4y +1 dy 2. Evaluate 0,

A: Given: ∫0234y+1dy Substitute, 4y+1=u dudy=4dy=14du =34∫udu ...........(1)

Q: Compute 3+r+1 dx x2

A: Given : ∫233x2+2x+1x2dx

Q: x² – 1 - Evaluate f dx x4 +1

A: We have to evaluate the integral: ∫x2-1x4+1dx This is special type of integration this will be…

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

A: we use integration by parts

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

A: Given ∫x(x2+1)3dx

Q: 2) Evaluate: x Inx dx

A:

Q: 4) Evaluate: §´ 12x – 1|dx

A: Given query is to find the value of the integral.

Q: 1. Evaluate : S (4x* + dx 2 S"(4x³ +)dx 0. x+1

A:

Q: 5 S Ix² x- 6|dx -5

A: The given integral,            ∫-55x2-x-6dx

Q: 2. Find b such that dx 1+x2 3

A:

Q: iii) So z dx 1+x2

A: Given: ∫01 x1 +x23dx To Evaluate given integral Proof: We will evaluate the given integral by…

Q: 3. Find [(5-x² +18) dx

A: Find     ∫5-x2+18x4dx