Question and Answers Forum

AllQuestion and Answers: Page 629

Question Number 156257 Answers: 0 Comments: 0

∫ ((xsin^(−1) (x^2 ))/(1−x^4 )) dx=?

$$\:\int\:\frac{{x}\mathrm{sin}^{−\mathrm{1}} \left({x}^{\mathrm{2}} \right)}{\mathrm{1}−{x}^{\mathrm{4}} }\:{dx}=? \\ $$

Question Number 156253 Answers: 1 Comments: 0

Question Number 156252 Answers: 1 Comments: 1

Question Number 156250 Answers: 0 Comments: 1

lim_(x→0) ((1−cos x (√(cos 2x)) ((cos 3x))^(1/3) ((cos 4x))^(1/4) )/x^2 ) =?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}\:\sqrt{\mathrm{cos}\:\mathrm{2x}}\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{3x}}\:\sqrt[{\mathrm{4}}]{\mathrm{cos}\:\mathrm{4x}}}{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$

Question Number 156248 Answers: 1 Comments: 0

Question Number 156244 Answers: 1 Comments: 0

solve the pairs of simultaneous equations ax−2y=2 x+3y=3 qy−px=(q^2 −p^2 )/pq py+qx=2

$${solve}\:{the}\:{pairs}\:{of}\:{simultaneous}\:{equations} \\ $$$${ax}−\mathrm{2}{y}=\mathrm{2} \\ $$$${x}+\mathrm{3}{y}=\mathrm{3} \\ $$$${qy}−{px}=\left({q}^{\mathrm{2}} −{p}^{\mathrm{2}} \right)/{pq} \\ $$$${py}+{qx}=\mathrm{2} \\ $$

Question Number 156240 Answers: 0 Comments: 3

∫^(π/2) _((−π)/2) ∣sin(x)∣ dx ∫^π _0 ∣cos(x)∣dx

$$\underset{\frac{−\pi}{\mathrm{2}}} {\int}^{\frac{\pi}{\mathrm{2}}} \mid{sin}\left({x}\right)\mid\:{dx} \\ $$$$\underset{\mathrm{0}} {\int}^{\pi} \mid{cos}\left({x}\right)\mid{dx} \\ $$

Question Number 156269 Answers: 0 Comments: 1

Question Number 156229 Answers: 0 Comments: 4

∫_0 ^( (π/4)) ln(sin(2x)+cos(3x)) dx

$$\: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\mathrm{ln}\left(\mathrm{sin}\left(\mathrm{2}{x}\right)+\mathrm{cos}\left(\mathrm{3}{x}\right)\right)\:{dx} \\ $$$$\: \\ $$

Question Number 156228 Answers: 1 Comments: 0

∫_0 ^( 1) ((log^3 (1−x^2 ))/x^3 ) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{log}^{\mathrm{3}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{3}} }\:{dx} \\ $$$$\: \\ $$

Question Number 156224 Answers: 0 Comments: 1

∫_0 ^( 1) (1/( (√(ln(x^2 )+1)) )) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\:\sqrt{\mathrm{ln}\left({x}^{\mathrm{2}} \right)+\mathrm{1}}\:}\:{dx} \\ $$$$\: \\ $$

Question Number 156222 Answers: 0 Comments: 1

∫_0 ^( 1) ln((sin(x)cos(x))^2 +1) dx

$$\: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{ln}\left(\left(\mathrm{sin}\left({x}\right)\mathrm{cos}\left({x}\right)\right)^{\mathrm{2}} +\mathrm{1}\right)\:{dx} \\ $$$$\: \\ $$

Question Number 156218 Answers: 1 Comments: 4

∫_0 ^( 1) (1/( (√(x(√(x^2 (√(x^3 (√(x^4 +1)))))))) )) dx

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\:\sqrt{{x}\sqrt{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{4}} +\mathrm{1}}}}}\:}\:{dx} \\ $$$$\: \\ $$

Question Number 156214 Answers: 0 Comments: 0

Question Number 156213 Answers: 0 Comments: 0

Ω =∫_0 ^1 log^2 (((Γ(x+1))/x)) dx = ?

$$\Omega\:=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{log}^{\mathrm{2}} \:\left(\frac{\Gamma\left(\mathrm{x}+\mathrm{1}\right)}{\mathrm{x}}\right)\:\mathrm{dx}\:=\:? \\ $$

Question Number 156206 Answers: 1 Comments: 0

Ω :=∫_0 ^( 1) (√x) (√(1−(√x) )) (√(1−(√(1−(√x) )))) dx=?

$$ \\ $$$$\Omega\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \sqrt{{x}}\:\sqrt{\mathrm{1}−\sqrt{{x}}\:}\:\sqrt{\mathrm{1}−\sqrt{\mathrm{1}−\sqrt{{x}}\:}}\:{dx}=? \\ $$

Question Number 156205 Answers: 0 Comments: 0

Question Number 156194 Answers: 0 Comments: 1

∫_0 ^( 1) (√(x(√(x^2 (√(x^3 .....(√x^n ))))))) dx n ∈ N

$$\: \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\sqrt{{x}\sqrt{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} .....\sqrt{{x}^{{n}} }}}}\:{dx} \\ $$$$\:\:\:\:\:\:\:\:\:{n}\:\in\:\mathbb{N} \\ $$$$\: \\ $$

Question Number 156180 Answers: 0 Comments: 0

Question Number 156334 Answers: 0 Comments: 1

Question Number 156178 Answers: 1 Comments: 0

Question Number 156177 Answers: 1 Comments: 0

∫_(−∞) ^∞ ((sin (x))/(x^2 +x+1))dx=?

$$\int_{−\infty} ^{\infty} \frac{\mathrm{sin}\:\left({x}\right)}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx}=? \\ $$

Question Number 156176 Answers: 1 Comments: 0

Question Number 156172 Answers: 3 Comments: 6

Question Number 156170 Answers: 2 Comments: 0

Question Number 156164 Answers: 1 Comments: 0

Pg 624 Pg 625 Pg 626 Pg 627 Pg 628 Pg 629 Pg 630 Pg 631 Pg 632 Pg 633

Contact: info@tinkutara.com