Ex 7.8, 20 - Chapter 7 Class 12 Integrals (Important Question)
Last updated at Dec. 16, 2024 by Teachoo
Chapter 7 Class 12 Integrals
Ex 7.1, 10
Important
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Class 12
Important Questions for exams Class 12
- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
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Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability
Transcript
Ex 7.8, 20 β«_0^1β(π₯ π^π₯+sinβ‘γππ₯/4γ ) ππ₯ Let F(π₯)=β«1β(π₯π^π₯+π ππ ππ₯/4)ππ₯ =β«1βγπ₯π^π₯ ππ₯+β«1βγsinβ‘(ππ₯/4) ππ₯γγ Solving I1 and I2 separately Solving π°π β«1βγπ₯π^π₯ ππ₯γ =π₯β«1βγπ^π₯ ππ₯ββ«1β[(ππ₯/ππ₯) β«1βγπ^π₯ ππ₯γ]ππ₯γ =π₯π^π₯ββ«1β(1.π^π₯ ππ₯)ππ₯ =π₯π^π₯ββ«1βγπ^π₯ ππ₯γ =π₯π^π₯βπ^π₯ =π^π₯ (π₯β1) Solving I2 β«1βγsinβ‘(ππ₯/4) ππ₯γ = 1/(π/4) (βcosβ‘(ππ₯/4) ) = (β4)/π cosβ‘(ππ₯/4) Therefore, F(π₯)=β«1βγπ₯π^π₯ ππ₯+β«1βγπ ππ π/4 π₯ ππ₯γγ =π^π₯ (π₯β1)β4/π cosβ‘(ππ₯/4) Now, β«_0^1β(π₯π^π₯+π ππ ππ₯/4) ππ₯=πΉ(1)βπΉ(0) =(π^1 (1β1)β4/π cosβ‘((π Γ 1)/4) )β(π^0 (0β1)+4/π πππ ((π Γ 0)/4)) =πΓ0β4/π πππ π/4β1(β1)+4/π cosβ‘0 =(β4)/( π) πππ π/4+1+4/π =(β4)/( π) 1/β2+1+4/π =(β2β2)/( π) +1+4/π =π+π/π β(πβπ)/π
