Definite Integrals
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Let [t] denote the greatest integer less than or equal to t. Then the value of ∫?²|2x-[3x]|dx is
Let [t] denote the greatest integer less than or equal to t. Then the value of ∫?²|2x-[3x]|dx is
The region represented by {z = x+iy∈C: |z|-Re(z)≤1} is also given by the inequality:
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The region represented by {z = x+iy∈C: |z|-Re(z)≤1} is also given by the inequality:
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|z|-Re (z)≤1 ⇒ √ (x²+y²)-x≤1 ⇒ √ (x²+y²)≤1+x ⇒ y²≤1+2x=2 (x+1/2).
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The value of the definite integral ∫π/?π/? dx / (1 + ³√tan2x) is:
The value of the definite integral ∫π/?π/? dx / (1 + ³√tan2x) is:
I = ∫ (π/24 to 5π/24) dx/ (1+³√tan2x). Using King's rule.
2I = ∫ (π/24 to 5π/24) dx = 4π/24=π/6. I=π/12.
Upvote <p><strong>The value of the definite integral ∫π/?π/? dx / (1 + ³√tan2x) is</strong></p>
If and be respectively the smallest and the largest values of in which satisfy the equation, , then is equal to:
If and be respectively the smallest and the largest values of in which satisfy the equation, , then is equal to:
2(cos²θ/sin²θ) - 5/sinθ + 4 = 0
(2sinθ - 1)(sinθ - 2) = 0
sinθ = 1/2 only
∴ θ = π/6, 5π/6
↓↓
θ?, θ?
∫(π/6 to 5π/6) cos²3θdθ = ∫(π/6 to 5π/6) (1+cos6θ)/2 dθ = π/3
Upvote The value of the integral ∫₋₁¹ log(x + √(x² + 1))dx is:
The value of the integral ∫₋₁¹ log(x + √(x² + 1))dx is:
log (x + √ (x²+1) is an odd function.
f (-x) = log (-x + √ (x²+1) = log (1/ (x+√ (x²+1) = -log (x+√ (x²+1) = -f (x).
Integral of an odd function over a symmetric interval is 0.
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