S (x2Vx3 – 3 + 70) dx

Q: 30. S = {-3 + 6x, 3x², 1 – 2x – x}

A: If vectors are L.D , then it will not form basis.

Q: 3 fx²³√₁² + x² dx X 2 a

A: Sol

Q: dx 4. 3 3 х3Vx2—9

A:

Q: V4x² – 49 (b) dx

A:

Q: r 4x² – 21x – 23 dx b) 4x+3 4x +5 c)

A:

Q: s(nx) < 2n

A:

Q: 6dx S: ³√x² x-

A:

Q: 7x d.x 2)3 (1 – x²)³

A:

Q: 2 (d²y + x3 = 0 -x | 2. 3.

A: We have to find the following conditions according to the given information

Q: S C3x-7 +5x -3 - x6 + 5x" t19) dx

A:

Q: V72+5/7³+3x -dx

A:

Q: S(x*-3x3 +- -2)dx = x(8x*-30x3+5x-80) + C 1 %3D 40

A: Consider the right hand side of the given equation. The integration formula is  ∫xn=xn+1n+1+c

Q: d'y d³y - dx5 dx3 = 24.

A: Solution :-

Q: Find the following

A: ∫(8x3+10x2-7x+5) dx

Q: d2y Find anž if 2x²-3y²=7 dx2

A: Given that 2x^3-3y^2=7

Q: dx Sx²+ 4 2. 多.区

A:

Q: d2/dx2 (5x + 1)4

A:

Q: (b) Evaluate 8x' +13x dx. (x² +2)²

A: Given integral is, ∫8x3+13xx2+22dx.   It is integrated as follows:   Apply the sum formula:…

Q: d²y Find dx2 if –10x – 6y = -6.

A:

Q: x3-2x2+7x-9 dx c.S x2

A:

Q: 2x³-4x-8 2. S; dx (x²-x)(x²+4)

A: Topic:- integration

Q: 53. g(x) = (4x² + 3x)e-7x %3D

A:

Q: x2 — х +1 dxp х2 + 2х + 2 x2.

A: Topic:- application of integration

Q: How would I do this?

A: Given integral can be written as

Q: x dx (7x2 + 3)

A:

Q: SX³V1+ 4x2 dx .3

A:

Q: e2x dx 4 + e4x 13.

A: We have to find the integral of the given function.

Q: The fx³5x dx is x²+2 {A} x − ² (x² + 2)² + C 5 {B} x + ²(x² + 2)² +C {C}-{In|x² {D}+In|x² +21+ C…

A: integration

Q: S dx b² +x4 - Evaluate

A:

Q: P(x) = -x³ - 4x + 2, D(x) = x + 1 x) *

A: To find- P(x)

Q: 11 (x7 – 5a*)"(7x6 – 15a?)dx 1 Determine: - 3x+5

A: See in the next step

Q: pð – xª + 4x3 – 4x² + 8x – 4 d.x - - (x² + 4)²

A:

Q: 28x-4 x 163*5 =16 х 16 Зx-5 %=D16 =16°x+2

A:

Q: - 48x3 – 80x2 – 70x – 126 dx Integrate: 16x2 + 25 + C

A:

Q: 4 5x2 Evaluate dx. TV3x2-1

A:

Q: d²y if 2x²-3y²=7 dx2

A: Differentiating both sides of the equation. 23x2-32ydydx=06x2-6ydydx=06ydydx=6x2dydx=x2y . . . . . .…

Q: fG) = x SCG) =3x+12 (S of ) Cx)=

A:

Q: f 12x -9x +2 dx 3.

A:

Q: 2. f (x²-16) ²/2 dx x3

A:

Q: Sxex² dx O 2+x²²/²/2/ HI HIN 6 1 2 HIN ex²+ + C + C + C

A:

Q: n(x) n c2x) dx -2 -3

A: Given integral is as below:

Q: 4 3/7) dx Find 4x* + - x6 + C

A:

Q: dx x²V4¬x* 4-2

A:

Q: dx 2. Evaluate -2 v2x2 + 8x + 10

A:

Q: 8x' +13x dx. (x² +2)² (b) Evaluate

A: Using partial fractions, Partial fractions of 8x3+13x(x2+2)2=Ax+Bx2+2+Cx+D(x2+2)2 as there is square…

Q: d4y Find Y=3X³-4X?+7X+10 dx4

A: Given y=3x3-4x2+7x+10 To find d4ydx4 Formulae used : dxn=nxn-1 dc=0, where c is a constant.…

Q: Find:

A: We rewrite the given integral as:

Q: dx Evaluate: x/9x² + 4

A: LetI=∫dxx9x2+4I=∫dxx(3x)2+22Put 3x=2tany  ⇒y=tan-1(3x2)differentiate…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: