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Question Number 51421 Answers: 2 Comments: 3

∫ ((tan^(−1) x)/x^2 ) dx

$$\int\:\:\frac{\mathrm{tan}^{−\mathrm{1}} \mathrm{x}}{\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$

Question Number 51420 Answers: 2 Comments: 0

∫ (e^(3x) /(1 + e^x )) dx

$$\int\:\:\frac{\mathrm{e}^{\mathrm{3x}} }{\mathrm{1}\:+\:\mathrm{e}^{\mathrm{x}} }\:\mathrm{dx} \\ $$

Question Number 51419 Answers: 1 Comments: 0

∫ ((√x)/(1 + (x)^(1/3) )) dx

$$\int\:\frac{\sqrt{\mathrm{x}}}{\mathrm{1}\:+\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}}}\:\mathrm{dx} \\ $$

Question Number 51394 Answers: 1 Comments: 0

∫ (1/(1 + (√(tan x)))) dx

$$\int\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\sqrt{\mathrm{tan}\:\mathrm{x}}}\:\:\mathrm{dx} \\ $$

Question Number 51389 Answers: 1 Comments: 2

Question Number 51372 Answers: 1 Comments: 1

Question Number 51368 Answers: 0 Comments: 8

Question Number 51367 Answers: 3 Comments: 0

Evaluate: cot^(−1) [(((√(1−sinx))+(√(1+sinx)))/((√(1−sinx))−(√(1+sinx))))] = ?

$${Evaluate}: \\ $$$$\mathrm{cot}^{−\mathrm{1}} \left[\frac{\sqrt{\mathrm{1}−\mathrm{sin}{x}}+\sqrt{\mathrm{1}+\mathrm{sin}{x}}}{\sqrt{\mathrm{1}−\mathrm{sin}{x}}−\sqrt{\mathrm{1}+\mathrm{sin}{x}}}\right]\:=\:? \\ $$

Question Number 51360 Answers: 0 Comments: 0

Question Number 51364 Answers: 0 Comments: 2

The value of x for which sin(cot^(−1) (1+x))=cos(tan^(−1) x) is ?

$${The}\:{value}\:{of}\:{x}\:{for}\:{which} \\ $$$$\mathrm{sin}\left(\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{1}+{x}\right)\right)=\mathrm{cos}\left(\mathrm{tan}^{−\mathrm{1}} {x}\right)\:{is}\:? \\ $$

Question Number 51356 Answers: 2 Comments: 1

Evaluate : tan {(1/2)cos^(−1) ((√5)/3)} ?

$${Evaluate}\:: \\ $$$$\mathrm{tan}\:\left\{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{−\mathrm{1}} \frac{\sqrt{\mathrm{5}}}{\mathrm{3}}\right\}\:? \\ $$

Question Number 51353 Answers: 4 Comments: 1

Question Number 51403 Answers: 0 Comments: 0

Question Number 51325 Answers: 1 Comments: 0

If a number of little droplets all of the same radius r coalesce to form a single drop of radius R.show that the rise in temperature is given by ((3T)/(pJ))((1/r)−(1/R)) where T is surface tension of water and J is mechanical equivalent of heat

$${If}\:{a}\:{number}\:{of}\:{little}\: \\ $$$${droplets}\:{all}\:{of}\:{the}\:{same}\: \\ $$$${radius}\:{r}\:{coalesce}\:{to} \\ $$$${form}\:\:{a}\:{single} \\ $$$${drop}\:{of}\:{radius}\:{R}.{show} \\ $$$${that}\:{the}\:{rise}\:{in}\:{temperature} \\ $$$${is}\:{given}\:{by} \\ $$$$\frac{\mathrm{3}{T}}{{pJ}}\left(\frac{\mathrm{1}}{{r}}−\frac{\mathrm{1}}{{R}}\right) \\ $$$${where}\:\:{T}\:{is}\:{surface}\:{tension} \\ $$$${of}\:{water}\:{and}\:{J}\:{is}\:{mechanical} \\ $$$${equivalent}\:{of}\:{heat} \\ $$

Question Number 51324 Answers: 2 Comments: 0

calculate ∫_0 ^(+∞) (dx/(1+x^(2 ) +x^4 ))

$${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}\:} \:+{x}^{\mathrm{4}} } \\ $$

Question Number 51321 Answers: 1 Comments: 0

A B C D is a parallelogram on the Argand plane. The affixes of A, B, C are 8 + 5i, − 7 − 5i, − 5 + 5i respectively . Find the affix of D

$$\mathrm{A}\:\mathrm{B}\:\mathrm{C}\:\mathrm{D}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{parallelogram}\:\mathrm{on}\:\mathrm{the}\:\mathrm{Argand}\:\mathrm{plane}.\:\mathrm{The}\: \\ $$$$\mathrm{affixes}\:\mathrm{of}\:\:\mathrm{A},\:\mathrm{B},\:\mathrm{C}\:\:\mathrm{are}\:\:\:\mathrm{8}\:+\:\mathrm{5i},\:\:−\:\mathrm{7}\:−\:\mathrm{5i},\:\:−\:\mathrm{5}\:+\:\mathrm{5i}\:\:\mathrm{respectively} \\ $$$$.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{affix}\:\mathrm{of}\:\:\mathrm{D} \\ $$

Question Number 51320 Answers: 1 Comments: 0

The points A, B, C represent the complex numbers z_1 , z_2 , z_3 respectively. And G is the centroid of the triangle A B C, if 4z_1 + z_2 + z_3 = 0, show that the origin is the mid point of AG.

$$\mathrm{The}\:\mathrm{points}\:\mathrm{A},\:\mathrm{B},\:\mathrm{C}\:\:\mathrm{represent}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{numbers}\:\:\mathrm{z}_{\mathrm{1}} ,\:\mathrm{z}_{\mathrm{2}} ,\:\mathrm{z}_{\mathrm{3}} \: \\ $$$$\mathrm{respectively}.\:\mathrm{And}\:\mathrm{G}\:\mathrm{is}\:\mathrm{the}\:\mathrm{centroid}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{A}\:\mathrm{B}\:\mathrm{C},\:\:\mathrm{if} \\ $$$$\mathrm{4z}_{\mathrm{1}} \:+\:\mathrm{z}_{\mathrm{2}} \:+\:\mathrm{z}_{\mathrm{3}} \:\:=\:\:\mathrm{0},\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mid}\:\mathrm{point}\:\mathrm{of}\:\:\mathrm{AG}. \\ $$

Question Number 51316 Answers: 0 Comments: 2