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Ex 7.9, 4 - Direct Integrate sin 2x dx from 0 to pi/4 - Definate Integration - By Formulae

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex7.9, 4 ∫_0^(π‘₯/4)β–’sin⁑2π‘₯𝑑π‘₯ Step 1 :- F(π‘₯)=∫1▒〖𝑠𝑖𝑛 2π‘₯ 𝑑π‘₯γ€— =1/2 (βˆ’π‘π‘œπ‘  2π‘₯) =(βˆ’1)/( 2) π‘π‘œπ‘  2π‘₯ Hence F(π‘₯)=(βˆ’1)/( 2) π‘π‘œπ‘  2π‘₯ Step 2 :- ∫_0^(πœ‹/4)▒〖𝑠𝑖𝑛2π‘₯ 𝑑π‘₯γ€—=𝐹(πœ‹/4)βˆ’πΉ(0) =(βˆ’1)/( 2) π‘π‘œπ‘ (2 Γ— πœ‹/4)βˆ’((βˆ’1)/( 2) π‘π‘œπ‘ (2 Γ—0)) =(βˆ’1)/( 2) π‘π‘œπ‘  πœ‹/2+1/2 π‘π‘œπ‘  0 =(βˆ’1)/( 2) Γ—0+1/2 Γ—1 = 𝟏/𝟐

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