Given 5 O a.) 5 O 5 f(x) dx = 12 and 6 [3f(x)+2g(x)]dx + f(x)dx O O b.) 10 c.) 40 5 d.) 32 = 12 and g(x)dx = -2, find the following:

Q: dx X*(4x+9)E

A: Given the integral ∫dxx24x4+932 We will use the the method of substitution to evaluate the integral.

Q: Let | a b. 2. =5, then 2a 26 2c 4g 4h 4i -e

A:

Q: (1+x)*dx X

A:

Q: E 689 to D F ...

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

Q: 9) Find 5-2x - dx

A: Given: Find d2dx25-2x for finding second derivative, we find first derivative then find derivative…

Q: (ex – 1)² | dx 3ex

A: We have to evaluate the integral

Q: Find f"-1) if f3) = (3x + 1)° . %3D O a) 9 O b) -27 c) 36 O d) -9

A: Given function is f(x)=y = (3x+1)3  We have to find f'(-1)

Q: Evaluate √2 4 √1-x² dx.

A:

Q: -d 23 X 2 9+хо dx

A: Given integral:- ∫-∞∞23x29+x6dx

Q: +). L x-1 dx -1x2+1

A:

Q: b) Evaluate:- 2 6² 44x² In(x) dx

A: Topic = Integration

Q: Find for y=x²³√x+1. dx A. 3x² 2√x+1 C. 3√x+1 B. D. (7x+6) 2√x+1 2√x+1 √26 +1

A:

Q: Q2: Evaluate the following b) fe-x³ dx

A:

Q: D. T= 18 W-1 3n² + 7n +5-3n gn+8+7n +7√√n 3

A:

Q: tan C3x ) dx

A:

Q: Evaluate √²+√2+1 dz. T3/2

A:

Q: 00 -36z2 Evaluate fe dx 12 16

A:

Q: Find 5 [(7x³ + 3x³) dz

A: use the algebraic property of integrals.

Q: Evaluate f x+3 x3+27 dx.

A: Our Aim is to evaluate the integral given below:-∫x3+27x+3dx -(i)

Q: Evaluate. dx 8x7 O A. + C O B. 1 +C 9ex9 1 C. + C 1 O D. 9 ex9 - 1 + C

A: The solution is :

Q: Solve for for the equation y = aln(x + )+ 4tan(;)– 2x O a. T O b. In(4 + x) O c. none of these O d.…

A:

Q: J x(x² + 3)5 dx

A:

Q: -dx. (3x² + 1)ª Evaluate -1 +C OA. 18(3x² + 1)³ O B, In(3x2 + 1)ª) +C 1 OC. + C 18(3x² + 1)³ x2 +C…

A: Given- ∫x3x2+14 To find- The value of the integral

Q: dx x lnx√9 ln²x-1 S

A: Given: I=∫dxxlnx9ln2x-1   ...(1)   As we know that; ∫1x2+1dx=tan-1x+C

Q: What is the value of sec¹(2)? A B C D 5 T 되어 3 -- 3 3 5T 3

A: Let sec-12=x  then     secx=2 As secant is the reciprocal of the cosine function, i.e.…

Q: 5л — 2 dx x2 +1 10.)

A:

Q: π/4 sec"x dx , Then 17 118- 16 16=. ..... ... Answer:

A: Solution:

Q: Find d²y 2 dx 11 y=¹1√√x

A:

Q: (-2,4) y 2 у = 4 − x2 -

A:

Q: Evaluate S 2 dx √x4+25

A: ∫1au+b du = 1alnau+b+C

Q: 1 3 + 4/7 ) dx Find x4 + C

A: Given:  ∫x2-1x+3x4+4xdxwe know that ∫A+Bdx=∫Adx+ ∫BdxThen,∫x2-1x+3x4+4xdx=∫x2dx-∫1xdx+∫3x4dx+∫4xdx…