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أكمل هذا البيان
إذا كان
f (x)=4x و g(x)=x3
فإن ∫[f(x) - g(x)] dx = ___________.
2x2−x33+c2x^2-\frac{x^3}{3}+c2x2−3x3+c
2x2−x44+c2x^2-\frac{x^4}{4}+c2x2−4x4+c
4x+x33+c4x+\frac{x^3}{3}+c4x+3x3+c
املأ الفراغ.
إذا كانت
f(x)=15x14
و
g(x)=x15،
إذن
∫[f(x)−g(x)]dx\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx∫[f(x)−g(x)]dx
x15−x1616+cx^{15}-\frac{x^{16}}{16}+cx15−16x16+c
x5−x66x^5-\frac{x^6}{6}x5−6x6
f(x)=8/x
g(x)=1/x2،
∫[f(x)−g(x)]dx=\int_{ }^{ }\left[f\left(x\right)-g\left(x\right)\right]dx=∫[f(x)−g(x)]dx=
8lnx+1x+c8\ln x+\frac{1}{x}+c8lnx+x1+c
lnx−1x+c\ln x-\frac{1}{x}+clnx−x1+c
7lnx+1x+c7\ln x+\frac{1}{x}+c7lnx+x1+c
f(x)= coscos41x
g(x)=e77x،
sinsin41x41+e77x77+c\frac{\sin\sin41x}{41}+\frac{e^{77x}}{77}+c41sinsin41x+77e77x+c
−coscos4x4+e7x7+c-\frac{\cos\cos4x}{4}+\frac{e^{7x}}{7}+c−4coscos4x+7e7x+c
sinsin41x41−e77x77+c\frac{\sin\sin41x}{41}-\frac{e^{77x}}{77}+c41sinsin41x−77e77x+c
f (x)=Cos x و g(x)=x2
إذن ∫[f(x) - g(x)] dx = ___________.
sinx+x33+c\sin x+\frac{x^3}{3}+csinx+3x3+c
sinx−x33+c\sin x-\frac{x^3}{3}+csinx−3x3+c
f(x)=x124
g(x)=x115،
x125125−x116116+c\frac{x^{125}}{125}-\frac{x^{116}}{116}+c125x125−116x116+c
x125125+x116116\frac{x^{125}}{125}+\frac{x^{116}}{116}125x125+116x116
x125125−x116116\frac{x^{125}}{125}-\frac{x^{116}}{116}125x125−116x116
f (x)=4x و g(x)=x2
2x2−4x+c2x^2-4x+c2x2−4x+c
2x2−x33+c2x^2-\frac{x^3}{3}+c2x2−3x3+c
x33+c\frac{x^3}{3}+c3x3+c
f(x)=3x
g(x)=x7،
−cotcot3x3−x88+c-\frac{\cot\cot3x}{3}-\frac{x^8}{8}+c−3cotcot3x−8x8+c
cotcot3x3+x88+c\frac{\cot\cot3x}{3}+\frac{x^8}{8}+c3cotcot3x+8x8+c
cotcot3x3+x88\frac{\cot\cot3x}{3}+\frac{x^8}{8}3cotcot3x+8x8
f(x)=8x
g(x)=e12x،
−cotcot8x8−e5x5+c-\frac{\cot\cot8x}{8}-\frac{e^{5x}}{5}+c−8cotcot8x−5e5x+c
tantan8x8−e12x12+c\frac{\tan\tan8x}{8}-\frac{e^{12x}}{12}+c8tantan8x−12e12x+c
tantan8x8+e12x12+c\frac{\tan\tan8x}{8}+\frac{e^{12x}}{12}+c8tantan8x+12e12x+c
إذا كانت f(x)=5x4
g(x)=12e12x،
x5−e12x+cx^5-e^{12x}+cx5−e12x+c
x5+e12x+cx^5+e^{12x}+cx5+e12x+c
x5−e2xx^5-e^{2x}x5−e2x
إنتهى الإختبار.