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IntegrationQuestion and Answers: Page 5
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Question and Answers Forum |
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IntegrationQuestion and Answers: Page 5 |
| ∫_0 ^(π/4) ∫_0 ^(π/4) ((tan(x^2 +y^2 )+sin(x^2 +y^2 ))/(tan(x^2 +y^2 )+cos(x^2 +y^2 )))dxdy |
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| ∫_( 0) ^( 1) x(√(x ((x ((x ((x ...))^(1/5) ))^(1/4) ))^(1/3) )) dx |
| ∫_(−1) ^1 (1/x)(√((1+x)/(1−x)))ln(((2x^2 +2x+1)/(2x^2 −2x+1)))dx |
| f(x)=ax |
| ∫(lnx)^2 dx |
| ∫((xe^x )/((x+1)^2 ))dx |
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| Prove:∫_0 ^(π/2) dφ∫_0 ^(π/2) f(sinθ cos θ)sinθ dθ=(π/2)∫_0 ^1 f(x)dx |
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| (i) ∫sec^5 θdθ (ii) ∫ (((√(tan θ)) dθ)/(cos θ)) |
| ∫∫∫_D (√(x^2 +y^2 +z^2 )) dv = ? D = x^2 +y^2 +z^2 <z |
| ∫(√((2sin^(−1) x−x(√(1−x^2 )))^2 +x^4 ))dx |
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| ∫_0 ^( s) (√(1−s^2 ))(1+(√(1−((x/s))^2 ))−(√(1−x^2 )))dx |
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| Let u^((1)) ,u^((2)) s.t. { ((u_(tt) ^((1)) =((∂^2 /∂x_1 ^2 )+(∂^2 /∂x_i ^2 ))u^((1)) )),((u^((1)) (x_1 ,x_2 ,0)=𝛙(x_1 ,x_2 ))),((u^((1)) (x_1 ,x_2 ,0)=0)) :}, { ((u_(tt) ^((2)) =((∂^2 /∂x_1 ^2 )+(∂^2 /∂x_2 ^2 )+c^2 )u^((2)) )),((u^((2)) (x_1 x_2 ,0)=0)),((u_t ^((2)) (x_1 ,x_2 ,0)=𝛙(x_1 ,x_2 ))) :} prove:u^((2)) (x_1 ,x_2 ,t)=(1/(2𝛑))∫∫_(𝛏_1 ^2 +𝛏_2 ^2 ≤t^2 ) ((e^(𝛏_2 c) u^((1)) (x_1 ,x_2 ,𝛏_1 )d𝛏_1 d𝛏_2 )/( (√(t^2 −𝛏_1 ^2 −𝛏_2 ^2 )))) |
| ∫_(Σ_(1≤i≤n) x_i ^2 ≤1) (Σ_(1≤i≤n) x_i ^2 )^m (Σ_(1≤i≤n) a_i x_i )^(2k) Π_(1≤i≤n) dx_i |
| ∫_(Σ_(1≤i≤n) x_i ^2 ≤R^2 ) Σ_(1≤i≤n) x_i (∂f/∂x_i )Π_(1≤i≤n) dx_i =? |
| ∫(e^(−ωu) +cos(u)−((sin(ωu))/e^u ))du |
| ∫_0 ^π ((xtanx)/(secx + tanx)) dx Solve the integral. |