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PRABODH PUBLICATION-निश्चित समाकलन -प्रश्नावली 19.4
- मान ज्ञात कीजिए: int(0)^(pi//2) (1)/(1+sqrt(tan x))dx
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- int(0)^(pi//2) (sin^(3//2))/(sin^(3//2)x+cos^(3//2)x) dx
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- int(0)^(pi//2) (sin^(n)x)/(sin^(n)x+cos^(n)x) dx
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- int(0)^(pi) (xsinx)/(1+sin x) dx
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- int(0)^(pi) x sin^(3)xdx
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- int(0)^(pi) x log sin x dx
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- int(0)^(pi/2) cos^(2)x dx
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- int(0)^(a) 1/(x+sqrt(a^(2)-x^(2))) dx
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- int(1)^(4) (sqrtx)/((sqrt(5-x)+sqrtx))dx
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- int(a//4)^(3a//4) (sqrtx)/((sqrt(x)+sqrt(a-x)))dx
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- int(0)^(pi//2) (2log cos x-log sin 2x)dx
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- int(0)^(pi) sin^(2)x cos^(3)xdx
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- int(0)^(pi) x/(1+cos alpha sin alpha) dx, 0 lt alpha lt pi
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- int(0)^(pi) xsin x cos^(4) xdx
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- int(-a)^(a) x^(3)sqrt(a^(2)-x^(2))dx
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- int(-pi)^(pi) x^(12)sin^(9)xdx
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- (i)int(-a)^(a) f(x) dx=2int(0)^(a) f(x)dx यदि f एक सम फलन है अर्थात ...
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- int(-pi//2)^(pi//2) sin^(3)xdx
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- int(-pi//2)^(pi//2) log((2-sinx)/(2+sinx))dx
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- int(0)^(pi) log(1-cos x)dx
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