Check sibling questions

Find f sin 2 x/ 9 - cos4 x dx

This question is similar to Example 42 - Chapter 7 Class 12 - Integrals

Slide4.JPG

Slide5.JPG
Slide6.JPG

This video is only available for Teachoo black users

Introducing your new favourite teacher - Teachoo Black, at only β‚Ή83 per month


Transcript

Question 1 – Choice 2 Find ∫1β–’γ€–sin⁑2π‘₯/√(9 βˆ’ cos^4⁑π‘₯ ) 𝑑π‘₯γ€—Now, ∫1β–’γ€–sin⁑2π‘₯/√(9 βˆ’ cos^4⁑π‘₯ ) 𝑑π‘₯γ€—=∫1β–’γ€–(𝟐 𝐬𝐒𝐧⁑𝒙 πœπ¨π¬β‘π’™)/√(πŸ— βˆ’(〖𝒄𝒐𝒔〗^πŸβ‘π’™ )^𝟐 ) 𝒅𝒙〗 Let 〖𝒄𝒐𝒔〗^πŸβ‘π’™=𝒕 Differentiating both sides w.r.t.π‘₯ 2 cos⁑π‘₯ Γ— βˆ’sin⁑π‘₯=𝑑𝑑/𝑑π‘₯ 𝒅𝒙=𝒅𝒕/(β€“πŸ 𝒄𝒐𝒔⁑𝒙 π’”π’Šπ’β‘π’™ ) Hence, our equation becomes ∫1β–’γ€–(𝟐 𝐬𝐒𝐧⁑𝒙 πœπ¨π¬β‘π’™)/√(πŸ— βˆ’(〖𝒄𝒐𝒔〗^πŸβ‘π’™ )^𝟐 ) 𝒅𝒙〗 =∫1β–’γ€–(2 sin⁑π‘₯ cos⁑π‘₯)/√(9 βˆ’ 𝑑^2 ) 𝑑π‘₯γ€— =∫1β–’γ€–(2 sin⁑π‘₯ cos⁑π‘₯)/√(9 βˆ’ 𝑑^2 )×𝒅𝒕/(β€“πŸ 𝒄𝒐𝒔⁑𝒙 π’”π’Šπ’β‘π’™ )γ€— =βˆ’βˆ«1▒𝑑𝑑/√((3)^2 βˆ’ (𝑑)^2 ) =βˆ’[sin^(βˆ’1)⁑〖𝑑/3+𝐢1γ€— ] =βˆ’π’”π’Šπ’^(βˆ’πŸ) 𝒕/πŸ‘+π‘ͺ It is of form ∫1▒〖𝒅𝒙/√(𝒂^𝟐 βˆ’ 𝒙^𝟐 )=π’”π’Šπ’^(βˆ’πŸ) 𝒙/𝒂+π‘ͺγ€— Replacing π‘₯ by 𝑑 and π‘Ž by 3, we get Putting back 𝒕=〖𝒄𝒐𝒔〗^πŸβ‘π’™ =βˆ’π’”π’Šπ’^(βˆ’πŸ) [𝟏/πŸ‘ 𝒄𝒐𝒔^𝟐 𝒙]+π‘ͺ

Davneet Singh's photo - Teacher, Engineer, Marketer

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.