Applications of Differentiation IV Lowersixth Science Mathematics

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Challenging integration questions for advanced high school

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Applications of Differentiation IV Lowersixth Science Mathematics


Froggy Jumps Applications of Differentiation IV Lowersixth Science MathematicsOnline version Challenging integration questions for advanced high school by YAKILI LMS 1 What is the integral of sin(x) cos(x) dx? a 1/2 cos^2(x) + C b cos^2(x) + C c 1/2 sin^2(x) + C 2 Integral of tan(x) dx equals? a sec^2(x) + C b -ln\|cos(x)\| + C c ln\|sin(x)\| + C 3 Integral of sec^2(x) dx is? a ln\|sec(x)\| + C b sec(x) + C c tan(x) + C 4 Compute ∫ e^x dx. a e^x + C b x e^x + C c e^{-x} + C 5 Integral of e^{ax} dx equals? a e^{ax} + C b a e^{ax} + C c e^{ax}/a + C 6 ∫ e^{2x} dx equals? a e^{2x}/2 + C b e^{x}/2 + C c 2 e^{2x} + C 7 Integrate cos^2(x) dx. a x/2 - 1/4 sin(2x) + C b 1/2 sin(x) + C c 1/2 x + 1/4 sin(2x) + C 8 Integral of sin^2(x) dx is? a 1/2 cos(2x) + C b 1/2 x - 1/4 sin(2x) + C c x/2 + 1/4 sin(2x) + C 9 ∫ sin(2x) dx equals? a -1/2 cos(2x) + C b cos(2x) + C c 1/2 sin(2x) + C 10 Compute ∫ cos(3x) dx. a sin(3x) + C b 1/3 sin(3x) + C c 1/3 cos(3x) + C 11 Integral of sec(x) tan(x) dx is? a sec(x) + C b tan(x) + C c ln\|sec(x)\| + C 12 ∫ tan^2(x) dx equals? a tan(x) + x + C b tan(x) - x + C c -tan(x) + x + C 13 Integral of 1/(1+x^2) dx is? a ln\|1+x^2\| + C b arcsin(x) + C c arctan(x) + C 14 Compute ∫ 1/(a^2 + x^2) dx. a 1/a arctan(x/a) + C b 1/a ln\|x+a\| + C c a/x + C 15 ∫ dx/(x^2) equals? a ln\|x\| + C b 1/x + C c -1/x + C 16 Integral of e^{ax} sin(bx) dx is derived via? a No method exists b Parts/complex numbers c Direct rule 17 ∫ e^{x} cos(x) dx equals? a e^{x}(sin x + cos x)/2 + C b e^{x} cos x + C c e^{x} sin x + C 18 Integrate e^{x} sin(2x) dx using tabular method; result is? a e^{x} (sin 2x + 2 cos 2x)/5 + C b e^{x} (sin 2x - 2 cos 2x)/5 + C c e^{x} sin 2x/2 + C 19 Completing the square: ∫ dx/(x^2 + 6x + 10) equals? a ∫ dx/[(x+3)^2+1] = arctan(x+3) + C b ln\|x+3\| + C c arctan(x) + C 20 What substitution helps ∫ dx/(x^2+ax+b)? a Partial fractions b Integration by parts c Complete the square 21 If I = ∫ e^{2x} dx, I =? a e^{2x}/2 + C b 2 e^{2x} + C c e^{x} + C 22 Integral of e^{x} cos(x) dx equals? a e^{x}(sin x + cos x)/2 + C b e^{x} cos x + C c e^{x} sin x + C 23 ∫ dx/(a^2 - x^2) equals? a 1/(a) arctanh(x/a) + C b ln\|a^2 - x^2\| + C c 1/(2a) ln\|(a+x)/(a-x)\| + C 24 Integrate cos(2x) dx. a sin(x) + C b cos(2x) + C c 1/2 sin(2x) + C 25 ∫ sec^2(2x) dx equals? a tan(2x)/2 + C b sec(2x) + C c tan(2x) + C 26 Compute ∫ e^{3x} dx. a e^{x}/3 + C b e^{3x}/3 + C c 3 e^{3x} + C 27 What is ∫ dx/(x^2+2x+2) dx after completing square? a ln\|x+1\| + C b arctan(x+1) + C c arctan(x) + C 28 ∫ 2x e^{x^2} dx substitute u = x^2 gives? a e^{2x} + C b e^{x^2} + C c x e^{x^2} + C 29 Integrate sin(3x) dx. a -1/3 cos(3x) + C b cos(3x) + C c 1/3 sin(3x) + C 30 ∫ e^{ax} dx with a=0.5 is? a e^{x} + C b e^{0.5x}/0.5 + C c 0.5 e^{0.5x} + C 31 Integral of tan(x) dx equals? a sec(x) + C b ln\|sin(x)\| + C c -ln\|cos(x)\| + C 32 ∫ cos(x) dx equals? a -sin(x) + C b sin(x) + C c cos(x) + C 33 ∫ dx/(1+x^2)^2 is best approached by? a trigonometric substitution b direct rule c partial fractions 34 Integral of e^{x} + e^{2x} dx equals? a e^{x} + C b e^{x} + e^{2x}/2 + C c e^{x}e^{2x} + C 35 Compute ∫ sin^2(x) dx using identity. a x/2 - sin(2x)/4 + C b x/2 + sin(2x)/4 + C c cos(2x)/2 + C 36 ∫ dx/(x^2) is? a -1/x + C b 1/x + C c ln\|x\| + C 37 Integrate cos(x) sin(x) dx. a 1/2 sin^2(x) + C b 1/2 cos^2(x) + C c cos^2(x) + C 38 ∫ e^{x} cosh(x) dx equals? a e^{x} cosh(x) + C b e^{x} sinh(x) + C c e^{x} + C 39 Integral of sec(x) dx is? a ln\|sec(x) + tan(x)\| + C b ln\|cos(x)\| + C c tan(x) + C 40 Compute ∫ dx/(x^2+1) dx. a arctanh(x) + C b arctan(x) + C c ln\|x^2+1\| + C 41 ∫ e^{x} dx equals? a e^{x} + C b x e^{x} + C c e^{-x} + C 42 ∫ dx/(x^2+4x+5) dx after completing square is? a arctan(x+2) + C b arctan(x) + C c ln\|x+2\| + C 43 Integral of tan^(-1)(x) is? a x^2/2 + C b arctan(x)/2 + C c x arctan(x) - 1/2 ln(1+x^2) + C 44 ∫ dx/(a^2 + x^2) with a>0 result is? a 1/a arctan(x/a) + C b ln\|x+a\| + C c a/x + C 45 Integrate sin(2x) dx. a -1/2 cos(2x) + C b 1/2 sin(2x) + C c cos(2x) + C 46 ∫ e^{2x} cos( x) dx technique is? a Direct rule b Integration by parts twice c Substitution only

Applications of Differentiation IV Lowersixth Science Mathematics

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Applications of Differentiation IV Lowersixth Science MathematicsOnline version

by YAKILI LMS

What is the integral of sin(x) cos(x) dx?

Integral of tan(x) dx equals?

Integral of sec^2(x) dx is?

Compute ∫ e^x dx.

Integral of e^{ax} dx equals?

∫ e^{2x} dx equals?

Integrate cos^2(x) dx.

Integral of sin^2(x) dx is?

∫ sin(2x) dx equals?

Compute ∫ cos(3x) dx.

Integral of sec(x) tan(x) dx is?

∫ tan^2(x) dx equals?

Integral of 1/(1+x^2) dx is?

Compute ∫ 1/(a^2 + x^2) dx.

∫ dx/(x^2) equals?

Integral of e^{ax} sin(bx) dx is derived via?

∫ e^{x} cos(x) dx equals?

Integrate e^{x} sin(2x) dx using tabular method; result is?

Completing the square: ∫ dx/(x^2 + 6x + 10) equals?

What substitution helps ∫ dx/(x^2+ax+b)?

If I = ∫ e^{2x} dx, I =?

Integral of e^{x} cos(x) dx equals?

∫ dx/(a^2 - x^2) equals?

Integrate cos(2x) dx.

∫ sec^2(2x) dx equals?

Compute ∫ e^{3x} dx.

What is ∫ dx/(x^2+2x+2) dx after completing square?

∫ 2x e^{x^2} dx substitute u = x^2 gives?

Integrate sin(3x) dx.

∫ e^{ax} dx with a=0.5 is?

Integral of tan(x) dx equals?

∫ cos(x) dx equals?

∫ dx/(1+x^2)^2 is best approached by?

Integral of e^{x} + e^{2x} dx equals?

Compute ∫ sin^2(x) dx using identity.

∫ dx/(x^2) is?

Integrate cos(x) sin(x) dx.

∫ e^{x} cosh(x) dx equals?

Integral of sec(x) dx is?

Compute ∫ dx/(x^2+1) dx.

∫ e^{x} dx equals?

∫ dx/(x^2+4x+5) dx after completing square is?

Integral of tan^(-1)(x) is?

∫ dx/(a^2 + x^2) with a>0 result is?

Integrate sin(2x) dx.

∫ e^{2x} cos( x) dx technique is?