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IntegrationQuestion and Answers: Page 34
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Question and Answers Forum |
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IntegrationQuestion and Answers: Page 34 |
| Find ∫x^5 (√(x^3 +1)) dx Answer: I= (2/(45)) (3x^3 −2) (√((x^3 +1)^3 )) + c |
| Help-me! Use double integral to find the area of the region bounded by the following curves given in the plane shown below: y^2 = 4x and x^2 = 4y |
| I= ∫ (x^2 /(sin (2arctan (e^x )))) dx , Find I |
| If f(x)=∫ (x^2 /(x^2 +tan x)) dx then ∫ ((tan x)/(x^2 +tan x)) dx =? |
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| C = ∫_0 ^(π/2) ((cos^2 x)/(4sin^2 x+cos^2 x)) dx =? |
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| Prove that ∫_0 ^(π/2) ((tan 2x)/( (√(sin^4 x+4cos^2 x)) −(√(cos^4 x+4sin^2 x))))=1 |
| ∫((tan (ln x).tan (ln (x/2)).tan (ln 2))/x)dx |
| calculate I=∫_0 ^( (π/4)) (( sin(x))/(1+ tan(2x))) dx = ? |
| ∫e^x^2 dx=? |
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| if I_n =∫xsin^n x dx and I_n = −((xsin^(n−1) x cosx )/n) +((sin^n x )/n^2 )+f(n)I_(n−2) then f(n) = ? |
| ∫_0 ^1 ((sin x(cos^2 x−cos^2 (π/5))(cos^2 x−cos^2 ((2π)/5)))/(sin 5x)) dx =? |
| ∫_(π/2) ^π (dx/((sin x−2cos x)^2 )) =? |
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| ∫((sin2x)/( (√(cos^4 x+1))))dx |
| Calculate 𝛗=∫_0 ^( 1) (( ln(x ))/(1 + x^( 2) )) dx =^? −G ∼ Solution ∼ 𝛗 = ∫_0 ^( 1) {Σ_(k=0) ^∞ (−1)^( k) x^( 2k) ln(x) }dx = Σ_(k=0) ^∞ (−1 )^( k) ∫_0 ^( 1) x^( 2k) ln(x) dx =^(i.b.p) Σ_(k=0) ^∞ (−1 )^( k) {[(x^( 1+2k) /(1+2k)) ln(x ) ]_0 ^1 −(1/(1+2k))∫_0 ^( 1) x^( 2k) dx } = Σ_(k=0) ^∞ (( (−1)^(1+k) )/(( 1 + 2k )^( 2) )) = − G ( Catalan constant ) ∴ 𝛗 = − G ■ m.n |
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| ∫ (dx/(cot^3 x sin^7 x)) =? |