Chapter 7 Class 12 Integrals
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Ex 7.8, 4 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by

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Ex 7.8, 4 ∫_0^(πœ‹/4)β–’sin⁑2π‘₯𝑑π‘₯ Let 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‘₯ Now, ∫_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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