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AllQuestion and Answers: Page 1517

Question Number 52991 Answers: 1 Comments: 1

Question Number 52988 Answers: 1 Comments: 0

∫ (x^2 /(√(1 + x^4 ))) dx

$$\int\:\frac{{x}^{\mathrm{2}} }{\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{4}} }}\:{dx} \\ $$

Question Number 52960 Answers: 1 Comments: 0

A wholesaler buys an article at“ $32 less 12.5%”. she then sells the article at a gain of 25% of her cost after allowing a 20% discount on her marked price. what is the marked price. please sir help me thanks

$${A}\:{wholesaler}\:{buys}\:{an}\:{article}\:{at}``\:\$\mathrm{32}\: \\ $$$${less}\:\mathrm{12}.\mathrm{5\%}''.\:{she}\:{then}\:{sells}\:{the}\:{article} \\ $$$${at}\:{a}\:{gain}\:{of}\:\mathrm{25\%}\:{of}\:{her}\:{cost}\:{after}\: \\ $$$${allowing}\:{a}\:\:\mathrm{20\%}\:{discount}\:{on}\:{her}\: \\ $$$${marked}\:{price}.\:{what}\:{is}\:{the}\:{marked}\: \\ $$$${price}. \\ $$$${please}\:{sir}\:{help}\:{me}\:{thanks} \\ $$

Question Number 52953 Answers: 1 Comments: 0

Can you pls help me with that but only by using the derivative of f(1) and not using the defined defivative of f(x) itself ? Thanks f(x) = x^2 − x f ′ (1) = ?

$$ \\ $$$$\mathrm{Can}\:\mathrm{you}\:\mathrm{pls}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{that}\:\mathrm{but}\:\mathrm{only} \\ $$$$\mathrm{by}\:\mathrm{using}\:\mathrm{the}\:\mathrm{derivative}\:\mathrm{of}\:{f}\left(\mathrm{1}\right)\:\mathrm{and}\:\boldsymbol{\mathrm{not}} \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{defined}\:\mathrm{defivative}\:\mathrm{of}\:{f}\left({x}\right)\:\mathrm{itself}\:? \\ $$$$ \\ $$$$\mathrm{Thanks} \\ $$$$ \\ $$$${f}\left({x}\right)\:=\:{x}^{\mathrm{2}} \:−\:{x} \\ $$$$ \\ $$$${f}\:'\:\left(\mathrm{1}\right)\:=\:? \\ $$

Question Number 52950 Answers: 1 Comments: 1

∫_( 0) ^(π/4) ((sin x+cos x)/(3+sin 2x)) dx =

$$\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{3}+\mathrm{sin}\:\mathrm{2}{x}}\:{dx}\:= \\ $$

Question Number 52949 Answers: 0 Comments: 4

If f(x) is an odd function, then ∫_( 0) ^π f (cos x) dx = 2∫_( 0) ^(π/2) f (cos x) dx

$$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{function},\:\mathrm{then} \\ $$$$\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:{f}\:\left(\mathrm{cos}\:{x}\right)\:{dx}\:=\:\mathrm{2}\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:{f}\:\left(\mathrm{cos}\:{x}\right)\:{dx} \\ $$

Question Number 52948 Answers: 2 Comments: 1

If f(x) =∫_( 1) ^x ((log t)/(1+t)) dt, then f(x)+f ((1/x) )=(1/2)(log x)^2

$$\mathrm{If}\:\:\:{f}\left({x}\right)\:=\underset{\:\mathrm{1}} {\overset{{x}} {\int}}\:\frac{\mathrm{log}\:{t}}{\mathrm{1}+{t}}\:{dt},\:\mathrm{then} \\ $$$$\:{f}\left({x}\right)+{f}\:\left(\frac{\mathrm{1}}{{x}}\:\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{log}\:{x}\right)^{\mathrm{2}} \\ $$

Question Number 52947 Answers: 1 Comments: 0

∫_( 0) ^π ((x tan x)/(sec x+cos x)) dx =