* Simplify the expression: * We can use the identities tan(x) = sin(x) / cos(x) and cosec(x) = 1 / sin(x) to rewrite the expression: sin(x) tan(x) + cos(x) cosec(x) = sin(x) * (sin(x) / cos(x)) + cos(x) * (1 / sin(x)) = sin^2(x) / cos(x) + cos(x) / sin(x) * Integrate using the formulas: * Now we can integrate each term separately using the formulas for sin(x) and cos(x): ∫ (sin^2(x) / cos(x) + cos(x) / sin(x)) dx = -∫ cos(x) dx + ∫ sin(x) dx = sin(x) - cos(x) + C Therefore, the integral of sin x tan x + cos x cosec x is sin(x) - cos(x) + C Bohot Jada Mehnat Lagi hai type karne me 😅
mera answer root log(cosx) kyu a ra hai? btw i just started integration today, (2026tard) ky ham values ko root me calc kr skte he kya? like my thing came out to be integral of root (sec x d(cosx))
@@prt-tanish5547bro please guide me i am new in class 11th. Which coaching should I take How should I start preparation and which books to follow? How did you prepared. Which mistakes I don't have to do
@@UdaySingh-rn4fx mathematics me ek X ki equation ke liye infinite number of values aa jati hai to ye to algebric me hai Phir bhi kaise nikala bta deta hu Sin.tan ko sin²/cos banaya aur cosec.cos ko cos/sin banaya Phir sin²/cos me sin² ko 1 - cos² se replace kiya aur cos/sin me let sin=t krke sovle kiya aur answer agya Log|sec + tan| - sin + log|sin| + c
Uss sawaal me direct product nikalo aur sin square theta ko 1-cos square theta kardo Aur dusre plus wale part me niche wale cos square theta se cos theta =t lelo phir go upar uska derivative hai phir game jaisa khelke kaam tamam kardo
Bruhh Pehle stanx ko sinx/cosx likho aur for sin¢2x ko 1-cos^2x likhdo jisse eqn bnjaaegi integration of secx+cosx Second part ke lie cot theta ka integration krdo Basic formulaes Ez maths
Mene socha easy hai karte hai phir dekha to 1 ghanta lag gya phir jab dobara short dekha to pata chala vo second part cosec cos tha mene cotcosec le liya
Change tan x into sinx/cosx and cosec x as 1/sinx then ; It becomes sin^2x / cos x + cosx /sinx then: Write sin^2x as 1-cos^2x then seprate and solve and ans will be ln|secx+tanx| + ln|sinx| - sinx + c ❤
§(tanx.sinx+cosecx.cosx)dx By using formula tanx=sinx/cosx Cosex=1/sinx So we can write it §(sinx. sinx /cosx+cosx .1/sinx We know that cosx/sinx=cotx and sin^2x=1-cos^2x So §(1-cos^2x/cosx+cotx)dx §secxdx-§cosxdx+§cotxdx ln|secx+tanx|+sinx+ln|sinx|+c😅
Limit not difined hai answer alag ho sakta hai Acording to me- Int(sinxtanx)=> Int(sin²x/cosx)=> Int(1-cos²x)/cosx=> Int(1/cosx - cos²x/cosx)=> Int(secx-cosx) Int(secx) - int(cos)=> Ln|tanx +secx| - sinx+c Similarly 2nd part
Solution: 1.Write the expression in terms of sinx and cosx. 2.Convert all sinx into cosx using [(sinx)^2 +(cosx)^2 =1] 3.Divide and break the fraction (a-b/c =a/c-b/c) Remaining: secx-cosx+cosecx.cotx Now integrate... Answer: ln(|secx+tanx|) - sinx - cosecx + c
Sir woh 2nd part easily ho jata hai.... Sirf first part ko sin and cos ke terms me likho aur fir take cos as t fir integration by parts... fir (1-t²) ko v manlo
Bhaiya aap iss question ko aise solve kijiye tantheta ko sin/cos break karlo aur likh do sinsquare theta /costheta then sintheta ko t man lo phir aapka expression t^2dt aa jayega phir udhar aap cosec theta ko 1/sintheta kardo wo banjayega cot theta aur ha pehle integration ko break karlena aapka answer phir ayega sin^3theta/3+ln sintheta +c 😊
Separate the integral sin theta*tan theta and cosec theta*cos theta And solve separately by integration by parts🤗method its so easy😅,you won't get trapped in this part ANSWER IS ln(secx+tanx)+ln(sinx)-sinx +c and i counted 1 as a constant so i ignored it,replace x with theta🤓
The correct answer to this question is ln(tanx+secx)+ln(sinx)-sinx+C we are taking theta is equal to x here since I don't know how to write theta in keyboard
For sinx tanx = break in sin cos, 1-cos sqaure/ sin , take sin t and alag alg solve khatam Now the next funtion break in sin cos, sin se multiply upr niche, 2sixcos=dt and sin sqaure x=t Khatam
dono ko alag alag integrate krlo right side wala to straight up {cotx} aur left side wala {secx} aur {-cosx} ban jayega ab bas jo bracket me hai unhe integrate krlo ans ln|secx+tanx| -sinx+log|sinx| aajaega.
Use by part Best method to solve integration is remember 15. Ways or type of inte. Method which ur good teacher gave u in notes Aur xam m 1 min phir last m inte ka ques ko time deena
Lekin ek minute... Chota bhai 12th mein hai isiliye integration ke questions solve kar raha aur bada bhai do saal se IIT ki taiyari kar raha hai matlab woh drop year mein hai, yeh kaise sambhav hai.
Bhaiya ek question tha.. Maine 11th and 12th me jee ka kuch bhi nhi padha but mujhe ab jee krna hi hai please aap batao ki kya kru . Mai bohot chote Village se hu mujhe koi bhi guide krne wala nhi hai
