Evaluate the integral (i) S3x3 sin 4x dx (ii) ſ In (x³ + x) dx (ii) cot-1 2x dx (iv) ſeax cos bx dx

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A: According to the guidelines issued by the company we are supposed to answer only first three sub…

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A: Here we have to find the integral.

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A: Given: I=∫sec2x+csc2xcos2xdx   Use the trigonometric identity; 1). sinx=1cscx 2). cosx=1secx And…

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A: SOLUTION-

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Q: Evaluate the integral. (Use C for the constant of integration.) x cos(6x) dx

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A: Let arccos(x)=t x=cos(t) dx=-sin(t)dt So the integral becomes - int t sin(t)dt =-t int sin(t)dt+int…

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Q: I. Evaluate the following integrals. 3.x5 dx V2 – x3 1. - 2* + e2" sin(2") dx sin(2") 2. 2x + 3 dx…

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Q: 7. Find the indefinite integral. (a) + sec , | dx = 4 In |x| + tan(x) +C (b) / )Lanr dx = In |In x|…

A: Given that: (a)∫4x+sec2xdx(b)∫1xlnxdx(c)∫x4-3x2+5x4dx

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A: Using identity         Sin2x+cos2x=1

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Q: 13. Find the integral using the u substitution method Jx(x+1)*dx

A: Solution of question as follow

Q: Evaluate the integral (i) S 3x3 sin 4x dx (ii) S In (x³ + x) dx

A: This section looks at Integration by Parts (Calculus). From the product rule, we can obtain the…

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 36 dx v3

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Q: Evaluate the integral. (Use C for the constant of integration.) 3 cos x dx 6 + sin x

A: Evaluate the integral.

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Q: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 5. Find the particular integral of d²y + dy - x2 + 2x + 4 dx2 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) cos−1(x) dx

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Q: Evaluate the integrals: (d) ∫(lnx)2dx. (e) ∫tan−1(3x)dx. (f)∫cos4(3x)dx.

A: We can evaluate the first two integrals by using  the integration by parts method. To evaluate…

Q: The value of the integral T/2 sin x dx cos(x)e- sin Jo is: Оа. 1-е-1 O a. O b. e- sin 1 O C. С. cos…

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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.