Question and Answers Forum

i\ ∫((sinx)/x)dx ii\ ∫((cosx)/x)dx iii\ ∫(1/(lnx))dx iv\ ∫(√(1−k^2 sin^2 x))dx v\ ∫(√(sinx))dx vi\ ∫sin(x^2 )dx vii\ ∫cos(x^2 )dx viii\ ∫xtanxdx ix\ ∫e^(−x^2 ) dx x\∫e^x^2 dx xi\ ∫(x^2 /(1+x^5 ))dx xii\ ∫((1+x^2 ))^(1/3) dx

$$\mathrm{i}\backslash\:\int\frac{\mathrm{sinx}}{\mathrm{x}}\mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{ii}\backslash\:\int\frac{\mathrm{cosx}}{\mathrm{x}}\mathrm{dx} \\ $$$$\mathrm{iii}\backslash\:\int\frac{\mathrm{1}}{\mathrm{lnx}}\mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{iv}\backslash\:\int\sqrt{\mathrm{1}−\mathrm{k}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$$$\mathrm{v}\backslash\:\int\sqrt{\mathrm{sinx}}\mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{vi}\backslash\:\int\mathrm{sin}\left(\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$$$\mathrm{vii}\backslash\:\int\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx}\:\:\:\:\:\:\mathrm{viii}\backslash\:\int\mathrm{xtanxdx} \\ $$$$\mathrm{ix}\backslash\:\int\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\backslash\int\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \mathrm{dx} \\ $$$$\mathrm{xi}\backslash\:\int\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{5}} }\mathrm{dx}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{xii}\backslash\:\int\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 95206 Answers: 1 Comments: 1

find the equation of the straight line which passes through the point of intersertion of the lines 4x+3y+19=0 and 12x−5y+3=0 and has a y_intercept of 2

$${find}\:{the}\:{equation}\:{of}\:{the}\:{straight}\:{line}\:{which} \\ $$$${passes}\:{through}\:{the}\:{point}\:{of}\:{intersertion}\:{of} \\ $$$${the}\:{lines}\:\mathrm{4}{x}+\mathrm{3}{y}+\mathrm{19}=\mathrm{0}\:{and}\:\mathrm{12}{x}−\mathrm{5}{y}+\mathrm{3}=\mathrm{0} \\ $$$${and}\:{has}\:{a}\:{y\_intercept}\:{of}\:\mathrm{2} \\ $$

Question Number 95202 Answers: 0 Comments: 4

Question Number 95342 Answers: 2 Comments: 0

determine the value of k such that the point A(4,−2,6) B(0,1,0) C(1,0,−5) and D(1,k,−2) lie on the same plane

$$\mathrm{determine}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{the}\:\mathrm{point}\:\mathrm{A}\left(\mathrm{4},−\mathrm{2},\mathrm{6}\right)\:\mathrm{B}\left(\mathrm{0},\mathrm{1},\mathrm{0}\right)\:\mathrm{C}\left(\mathrm{1},\mathrm{0},−\mathrm{5}\right) \\ $$$$\mathrm{and}\:\mathrm{D}\left(\mathrm{1},\mathrm{k},−\mathrm{2}\right)\:\mathrm{lie}\:\mathrm{on}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{plane}\: \\ $$

Question Number 95341 Answers: 0 Comments: 0

Q) A light falls on two slits 0.15 mm apart.An interference pattern is produced on a screen 60 cm from the slits, if the distance between the second and the fifth bright bands (frings) is 0.7 cm. Calculate the avelength of the used light. solution: Δy_(n=2→n=5) =0.7⇒Δy=0.7/3=0.233×10^(−2) m Δy=((sλ)/d) ⇒λ=((dΔy)/s)=((0.15×10^(−3) ×0.233×10^(−2) )/(60×10^(−2) )) =5.83×10^(−7) =583 nm

$$\left.\mathrm{Q}\right)\:\mathrm{A}\:\mathrm{light}\:\mathrm{falls}\:\mathrm{on}\:\mathrm{two}\:\mathrm{slits}\:\mathrm{0}.\mathrm{15}\:{mm}\:\mathrm{apart}.\mathrm{An}\:\mathrm{interference}\:\mathrm{pattern} \\ $$$$\mathrm{is}\:\mathrm{produced}\:\mathrm{on}\:\mathrm{a}\:\mathrm{screen}\:\mathrm{60}\:{cm}\:\mathrm{from}\:\mathrm{the}\:\mathrm{slits},\:\mathrm{if}\: \\ $$$$\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{second}\:\mathrm{and}\:\mathrm{the}\:\mathrm{fifth}\: \\ $$$$\mathrm{bright}\:\mathrm{bands}\:\left(\mathrm{frings}\right)\:\mathrm{is}\:\mathrm{0}.\mathrm{7}\:{cm}.\:\mathrm{Calculate}\:\mathrm{the}\: \\ $$$$\mathrm{avelength}\:\mathrm{of}\:\mathrm{the}\:\mathrm{used}\:\mathrm{light}. \\ $$$$\boldsymbol{{solution}}: \\ $$$$\Delta{y}_{{n}=\mathrm{2}\rightarrow\mathrm{n}=\mathrm{5}} =\mathrm{0}.\mathrm{7}\Rightarrow\Delta{y}=\mathrm{0}.\mathrm{7}/\mathrm{3}=\mathrm{0}.\mathrm{233}×\mathrm{10}^{−\mathrm{2}} \:{m} \\ $$$$\Delta{y}=\frac{{s}\lambda}{{d}}\:\Rightarrow\lambda=\frac{{d}\Delta{y}}{{s}}=\frac{\mathrm{0}.\mathrm{15}×\mathrm{10}^{−\mathrm{3}} ×\mathrm{0}.\mathrm{233}×\mathrm{10}^{−\mathrm{2}} }{\mathrm{60}×\mathrm{10}^{−\mathrm{2}} } \\ $$$$=\mathrm{5}.\mathrm{83}×\mathrm{10}^{−\mathrm{7}} =\mathrm{583}\:{nm} \\ $$

Question Number 95199 Answers: 1 Comments: 0

∫_(−π) ^π cosxln((1+x)/(1−x)) dx=?

$$\int_{−\pi} ^{\pi} {cosxln}\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\:{dx}=? \\ $$

Question Number 95198 Answers: 1 Comments: 0

∫(√((x+2)/(x−3)))dx=?

$$\int\sqrt{\frac{{x}+\mathrm{2}}{{x}−\mathrm{3}}}{dx}=? \\ $$

Question Number 95182 Answers: 1 Comments: 0

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