Question

find the antiderivative of 3 X square + 4 x cube​

Answer 1

Answer:





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Question



Write an anti derivative for each of the following functions using the method of inspection:

i) cos 2x

ii) 3x2+4x3

iii) x1,x=0

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Solution



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(i) Let F(x)=2sin2x

that

f′(x)2×2cos2x

=cos2x

therefore quantitative of cos2xis2sin2x

(ii) Let F(x)=x3+x4

then F′(x)=3x2+4x3

thus quantitative of  3x2+4x3

is x3+x4

(iii) Let  f(x)=logx

F(x)=x1

therefore quantitative of x1 is logx

Step-by-step explanation:

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Answer 2

Answer:

⇒ ∫3x² + ∫4x³ = x³ + x⁴

Step-by-step explanation:

Have to find the anti-derivative of 3x²+4x³

⇒ ∫3x² + ∫4x³

⇒ 3∫x² + 4∫x³

∫x² = x³/3

∫x³ = x⁴/4

⇒ ∫3x² + ∫4x³ = 3(x³/3) + 4(x⁴/4)

⇒ ∫3x² + ∫4x³ = x³ + x⁴