11. Find the area under the graph of f(x)= sin 2x cos 2x on the interval [0, 41.

Q: Evaluate the integral. /2 15 cos Jo s x dx

A: Given:          ∫0π215cos5x dx        =15∫0π2cos5x dx         =15∫0π2cos2x2cosx dx…

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

A: see below the calculation and answer

Q: Evaluate the integral. Зп /4 6 sin (x) cos (x) dx Jn/2

A:

Q: 8. Evaluate the integral. sin x xp. 4+ cos x

A:

Q: Evaluate the indefinite integral.

A:

Q: 7. Find the area between f(x)=-x² + 4x and g(x) = x² - 6x +5 over the interval 0≤x≤1 Ei..

A:

Q: cos®xdx CoS Xx, 0.

A: We have to evaluate the integral.

Q: 1 * dx 1+ sin x + cos x

A:

Q: (x2 + 2x) cos x dx

A: Given,         ∫x2+2xcosxdx

Q: prove f sinh(x) cosh(x) dæ = } cosh(2x) + C" %3D

A: Evaluate the given integral as follows. ∫sinhxcoshxdx=12∫2sinhxcoshxdx=12∫sinh2xdx…

Q: Obtain a formula that expresses the integral ∫cosn x dx

A:

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

A:

Q: Evaluate the indefinite integral sin (2)cos"(2)dz 4

A:

Q: Evaluate the integral. S-3x cos(2x) dx

A:

Q: Find integral of sin^2 (x/2) dx with bounds of 0 to pi

A: Find the integral of sin^2 (x/2) dx with the bounds 0 to π.

Q: O Approximate So In (3 + sin x)dx using Simpson's Rule with(n = 4 %3D

A:

Q: 2. Find the following indefinite integral. et cos cos (3x)dx

A: To evaluate ∫excos(3x) dx

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

A: Given integral to evaluate  ∫cos2xsin2xdx substitute sin2x=2sinxcosx ∫cos2xsin2xdx=∫cos2x2sinxcosxdx…

Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: Find the integral of 12 sin^5 x cos^5 x dx if the lower limit is O and the upper limit is T/2.

A:

Q: Find the indefinite integral. ∫(x2 cos x)dx

A: The given integral is ∫x2cosx  dx. Let u=x2  and   dv=cosx dx. This implies that du=2xdx  and…

Q: 7. Find the integral of the hyperbolic function below. 6 sin(x) cosh[cos(x)] dx

A: Evaluate: ∫6 sinx coshcosx dx

Q: Find the indefinite integral.

A: Given,∫2sinxcosxdxwe need to find the indefinite integral

Q: The approximation of 1 = cos(x+10) dx using composite Simpson's rule with n-3 is: 1.01259 3.25498

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: Find the indefinite integral ∫cos 2x cos 6x dx

A: Given integration as I=∫cos 2x cos 6x dx Since  2cos 2x cos 6x=cos 6x+2x+cos 6x-2x…

Q: Find the indefinite integral. | x cos 9x² dx

A: Given : ∫xcos(9πx2)dx

Q: Evaluate the definite integral. T/2 esin(x) cos(x)dx

A:

Q: use the method for odd powers to evaluate the integral.

A:

Q: 3. 6x° cos (x*) dx

A:

Q: Evaluate the definite integral. 1 6 cos(at/2) dt

A: Given:        ∫016cosπt2dt Taking constant out      =6∫01cosπt2dt substitute u=πt2…

Q: Obtain a formula that expresses the integral [cos". cos" x dx

A:

Q: What is the area between the graphs of the functions f (x) = 5 sin x and g (x) = e x − 3, between x…

A: Graph of the given system is:

Q: Consider the following functions. f(x) g(x) = 8 sin x = 8 cos 2x 6 Sketch the region bounded by the…

A: Solved below

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 integral cos (x) sin(x) dx using the substitution u = = cos(x). | cos" (x) sin(x) dx 13…

A: topic - integration

Q: Find the indefinite integral ∫ 2sin x cos x dx

A: The given integral is ∫2sin(x)cos(x)dx

Q: Evaluate the integral. T/2 9 sin2(x) cos2(x) dx

A:

Q: (x2 + 8x) cos(x) dx

A: We have to find the integral As per guideline we have to solve one question Please repost other…

Q: Evaluate integral. integral 0 to pi/4 (1+cos^2theta/ cos^2) dtheta

A:

Q: Evaluate the indefinite integral. cos x dx (sin x)27

A: Let's find.

Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: 2T COs x dx

A:

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

A:

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

A:

Q: Evaluate the following integral cln 2 cosh x dx. sinh² 0. x + 4 sinh x + 2

A:

Q: Obtain a "reduction" formula that expresses the integral cos" x dx in terms of an integral of a…

A: Integration by parts: If u is first function and v is second function then: ∫u(x) v(x) dx=u(x)∫v(x)…

Q: 6 Evaluate the improper integral, if exists : dx (5 – x)3 -00

A:

Q: Only one of these calculations is correct to evaluate the definite integral Vx+1 dx Using the…

A:

Q: Evaluate the integral cos (x) sin(x) dx 13 using the substitution u = cos(x). cos(x) sin(x) d.x ,13…

A: I am going to solve the given problem by using some simple calculus to get the required result.

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

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…