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AllQuestion and Answers: Page 1950

Question Number 12773 Answers: 1 Comments: 0

Question Number 12768 Answers: 1 Comments: 0

∫ ((sec x)/(tan^2 x)) dx

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

Question Number 12766 Answers: 1 Comments: 0

∫ (dx/(1 + tan x))

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

Question Number 12763 Answers: 0 Comments: 0

Solve simultaneously 2x + y − z = 8 ........... equation (i) x^2 − y^2 + 2z^2 = 14 .......... equation (ii) 3x^3 + 4y^3 + z^3 = 195 ........... equation (iii)

$$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$\mathrm{2x}\:+\:\mathrm{y}\:−\:\mathrm{z}\:=\:\mathrm{8}\:\:\:\:\:\:\:\:...........\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{2z}^{\mathrm{2}} \:=\:\mathrm{14}\:\:\:\:\:\:\:..........\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{3x}^{\mathrm{3}} \:+\:\mathrm{4y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:=\:\mathrm{195}\:\:\:\:\:\:\:\:\:...........\:\mathrm{equation}\:\left(\mathrm{iii}\right) \\ $$

Question Number 12760 Answers: 2 Comments: 0

Question Number 12753 Answers: 1 Comments: 0

evaluate ∫(√((sin x)))dx

$${evaluate}\:\int\sqrt{\left(\mathrm{sin}\:{x}\right)}{dx} \\ $$

Question Number 12752 Answers: 0 Comments: 0

Let V and W be 4 dimensional subspaces of a 7 dimensional vector space X. Which of the following CANNOT be the dimension of the subspace V∩W. (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

$$\mathrm{Let}\:\mathrm{V}\:\mathrm{and}\:\mathrm{W}\:\mathrm{be}\:\mathrm{4}\:\mathrm{dimensional}\:\mathrm{subspaces}\:\mathrm{of}\:\mathrm{a}\:\mathrm{7}\:\mathrm{dimensional}\:\mathrm{vector}\:\mathrm{space}\:\mathrm{X}. \\ $$$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{CANNOT}\:\mathrm{be}\:\mathrm{the}\:\mathrm{dimension}\:\mathrm{of}\:\mathrm{the}\:\mathrm{subspace}\:\mathrm{V}\cap\mathrm{W}. \\ $$$$\left(\mathrm{A}\right)\:\mathrm{0}\:\left(\mathrm{B}\right)\:\mathrm{1}\:\left(\mathrm{C}\right)\:\mathrm{2}\:\left(\mathrm{D}\right)\:\mathrm{3}\:\left(\mathrm{E}\right)\:\mathrm{4} \\ $$

Question Number 12744 Answers: 1 Comments: 0

∫_( e^(−3) ) ^( e^(−2) ) (1/((x)log(x))) dx = ?

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

Question Number 12743 Answers: 2 Comments: 0

What is the area of eqilateral triangle whose inscribed circle has a radius 2

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{eqilateral}\:\mathrm{triangle}\:\mathrm{whose}\:\mathrm{inscribed}\:\mathrm{circle}\:\mathrm{has}\:\mathrm{a}\:\mathrm{radius}\:\mathrm{2} \\ $$

Question Number 12742 Answers: 1 Comments: 0

Prove that ∫ (dx/((x +1)^2 (√(x^2 + 2x +2)))) = ((−(√(x^2 + 2x + 2)))/(x + 1)) + C

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\int\:\frac{{dx}}{\left({x}\:+\mathrm{1}\right)^{\mathrm{2}} \:\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\mathrm{2}}}\:=\:\frac{−\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\:\mathrm{2}}}{{x}\:+\:\mathrm{1}}\:+\:{C} \\ $$

Question Number 12740 Answers: 1 Comments: 0

∫∣x∣ dx