12Findthe integral using an appraimate triganametrit Substitution. S 25x2-4dx

Q: dx x²√4x² O a. √4-x² 4x √4+x² X + C + C O b. O d. 4x √4-x² X /4+x² + C + C

A:

Q: 4. Evaluate the trigonometric integral. sin³ 0 cos? 0 de 3

A: Given that,

Q: Use the substitution a = 2 sect to evaluate the integral dz

A:

Q: X +25 x = 5 tan(0) 'xp

A: Given: - The Indefinite integral is,  ∫x3x2+25dx, where x=5tanθ To find: - The solution of the given…

Q: In trigonometric substitution where the integral involves va? + u², what must be the value of the…

A:

Q: Consider the integral x2 dæ, (x² + a²)³/2 where a is a positive real number.

A:

Q: Use an appropriate trigonometric identity and substitution to evaluate the integral: tan’ r sec rdr

A: Given Indefinite integral as follows As we know that

Q: 1 r+ 2 2-4x +9 2x +5 dx e)) + 8x + 25 =dx V3-2x-x 1 1 dx 25+ 9x J100-x² ²

A: These three parts can be solved using the formulas of some special integrals

Q: what trig substitution is correct for 7 tan e 7sine 49sin e 7 sece 49 tane 49sece V49 9-r Write the…

A: Let I=∫49-x24x2dx To solve the above integral let substitute x=7sinθ…

Q: tan ³x sec4x dx. Use trigonometric group

A:

Q: e dx 6+ e2

A:

Q: Evaluate the integral using the methods covered in the text so far:                    ∫ sec2 θ tan7…

A: Given:                ∫sec2θ tan7θ dθ Apply u-substitution u=tan θ⇒du=sec2 θ dθ              =∫u7 du…

Q: Solve S 18x-17 √9x²-18x+18 dx.

A:

Q: dx '9 + 8x – x² + 6^ -

A: Given: From the above expression,

Q: dx x* +3

A:

Q: "/2 cot5 x csc³ x dx Sal

A:

Q: Solve the integral 10 sin? 5x cos4 10x dx 8.

A: Given integral is, I=∫0π10sin25xcos410xdx. Substitute, 5x=t. ⇒dx=dt5. Now, limits of t will be, For…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.