5) find the integral J8 sin 2x * cos2x dx

Q: Find the indefinite integral. ∫(5 cos x − 2 sec2 x) dx

A: We first separate the integrals then integrate.  C=integrating constant

Q: Evaluate the integrals ∫sin 3x sin 3x dx

A:

Q: Solve: The indefinite integral of the integrand (cos x/1+sin2 x) dx

A:

Q: sec 3x tan² 3x dx

A:

Q: Evaluate the integrals ∫sec2 x tan2 x dx

A:

Q: Evaluate the definite integral. π/2 1- cos(2x) dx

A: Answer:-(1) Given the integral,     ∫sin2x cos22x dx=∫44*sin2x cos22x dx…

Q: Evaluate the integral. |cos 7x cos 3x dx

A: The given integral ∫cos7xcos3xdx.

Q: Find the integral of x^2 * cos(4x) dx.

A: To compute the indefinite integral.

Q: Evaluate the integrals ∫sin4 2x cos 2x dx

A: I=∫ Sin4 2x Cos 2x dxLet Sin 2x=t2 Cos 2x dx=dtCos 2x dx=dt2

Q: S sin x In(cosx) dx

A: To evaluate the integral: I=∫sin x(ln (cos x)) dx Substitute  cos x=t⇒-sin x dx=dt⇒sin x dx=-dt

Q: •3 sin (7|3 – 2x) dx

A:

Q: Evaluate the integral.  integral  sec 2 x  tan  3 x  dx

A: Consider the following integral:

Q: Evaluate the integral: CT/2 cos² (4x) sin³ (4x) dx.

A:

Q: 1 x² cos(x³) dx CoS

A:

Q: Evaluate the integrals ∫cos5 x sin5 x dx

A: Given integral:

Q: Solve the integral. sin x dx 10. cos2 x + cOs x – 2

A: Given: ∫sinxcos2x+cosx-2 Let u=cosx, thendudx=-sinx and dx=-1sinxdu.…

Q: Evaluate the integral.  integral  sec 5 x  tan  4 x  dx

A: Integration:                    ∫sec5(x)tan4(x)dx                    Solving using Trigonometric…

Q: Compute the integral (3)/(1+x^2)-sec(x)tan(x)+2^xdx

A: The given integral is: ∫31+x2-secx tanx+2x dx ∫31+x2-sec x tan x+2x dx=3∫11+x2dx-∫sec x tan x dx+∫2x…

Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: Evaluate the integral. integral  cos 3x  sin 2x dx

A:

Q: Evaluate the integral. integral 0  to pie /2     sin 3x  cos 2x dx

A: Consider,

Q: Evaluate the integrals for 16 sin²x cos²x dx

A: ∫16sin2xcos2x dx=∫4(4sin2xcos2 x) dx                                 =4∫(2sinxcos x)2 dx…

Q: sin x + 10(csc x)² dx

A: To compute: ∫(sin x+10(csc x)2)dx

Q: set up an integral ....bounds x=3pi/4 x=-pi/4 y=-sinx and y=-cosx

A: GRAPH

Q: Evaluate the integral S cos ³ x + 8 sin x cos³² x + 6s in ² x dx; cosx #0 2 cos²x

A:

Q: Evaluate the integrals sec 3x tan 3x dx

A: As per guidelines, i can answer only one question.

Q: Compute the indefinite integral. ∫(1−sin2x)/(cosx) * dx

A: The given integral is,

Q: Find the indefinite integral.∫ 8x cos2x dx

A: To integrate the indefinite integral: ∫8xcos2xdx

Q: Evaluate the integral.  integral  sec3  x  tan  4 x  dx

A:

Q: Evaluate the integral.  integral  sec  6x  tan  x  dx

A: Given integral  sec  6x  tan  x  dx

Q: Evaluate the integrals. ∫x sin x2 cos8 x2 dx

A: Given,         ∫xsinx2cos8x2dx

Q: Find the indefinite integral. ∫cos3( x/3)   dx

A:

Q: 8 (a) To evaluate the integral J cos xdx by using the reduction formula of Cosine function.

A: We have to use cosine reduction formula.

Q: Evaluate the integrals ∫16 sin2 x cos2 x dx

A:

Q: Calculate the integral ∫dx / sin4x+cos4x.

A: Given,   .

Q: cos (6x) cos (3x)dx

A: Solution :∫cos6xcos3xdxNote…

Q: Evaluate the integrals ∫cos x cos 7x dx

A: To integrate: ∫cosxcos7xdx.  We know that cosacosb=12sina+b-sina-b. Therefore, using the above…

Q: Find the indefinite integral ∫ cos2 x sin4 x dx

A: Given: I=∫cos2xsin4xdx we know that ∫sinnxdx=n-1n∫sinn-2xdx-cosxsinn-1xn                   ..1

Q: Evaluate the indefinite integral. ∫cos(2x)(9−sin(2x))^(1/2)dx

A: Given:

Q: Evaluate the integrals ∫cos 3x cos 4x dx

A: Evaluate ∫ cos 3xcos 4xdx

Q: Evaluate the integrals ∫sin3 x cos4 x dx

A:

Q: 4. Prove using the results concerning iterated integrals that In 5 dx = 4 sin? x

A: Given:-                 To prove the result concerning iterated integrals that…

Q: Find the indefinite integral.∫cos2 3x dx

A: To evaluate the indefinite integral ∫cos23x. Solution: The given integral is ,∫cos23x Multiply both…

Q: Evaluate the integral of sin(4x) cos(3x) dx

A: We have to use 2sinAcosB= sin(A+B)+sin(A-B) formula to simplify first.

Q: Evaluate the integrals ∫cos3 2x sin5 2x dx

A: Evaluate: ∫cos32xsin52xdx

Q: 14. Use a suitable change of variables to determine the indefinite integral. fsin²xcos³ xdx (Hint:…

A:

Q: Evaluate the integrals ∫(tan x)-3/2 sec2 x dx

A:

Q: Evaluate the integral ( sin(In(2+2x)) x+1 dx

A: Given: ∫sinln2+2xx+1dx

Q: Evaluate the integrals ∫sin3 x cos3 x dx

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.