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vodka [1.7K]
3 years ago
6

Find

="absmiddle" class="latex-formula"> if y=\int\limits^a_b {e^{t}tan } \,t dt, where a=x^3, b=3x

Mathematics
2 answers:
OLga [1]3 years ago
6 0

Step-by-step explanation:

Use the second fundamental theorem of calculus.

If y = ∫ₐᵇ f(t) dt, then dy/dx = f(b) db/dx − f(a) da/dx

dy/dx = e^(x³) tan (x³) (3x²) − e^(3x) tan (3x) (3)

dy/dx = 3x² e^(x³) tan (x³) − 3 e^(3x) tan (3x)

vitfil [10]3 years ago
3 0

Answer:

3[x²(e^x³)(tan(x³) - (e^3x)tan(3x)]

Step-by-step explanation:

Derivative of x³ = 3x²

Derivative of 3x = 3

3x²(e^x³)(tan(x³) - 3(e^3x)tan(3x)

3[x²(e^x³)(tan(x³) - (e^3x)tan(3x)]

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