Mühendislik ve Doğa Bilimleri Fakūltesi 2019-2020 Bahar Dōnemi Genel Matematik II Vize Smav Ödev Sorular
04-12 Mays 2020
Adi - Soyadı:
Numarası :
Bōlümũ :
1) $\int \frac{\sin x}{\cos^{7} x} d x$ integralini hesaplaymuz.
2) $\int_{0}^{1} \frac{x \arctan (x^{2})}{1 + x^{4}} d x$ integralini hesaplayiniz.
3) $y = x^{2}$ ile $y = 8 - x^{2}$ eğrileri tarafindan smurlanan bōlgenin alanum bulunuz
4) $\int \cos^{6} x \sin x \tan^{2} x d x$ integralini hesaplaymiz.
5) $\int \frac{2 x + 5}{x^{3} + 5 x} d x$ integralini hesaplayınz.
6) $f (x) = \int_{1}^{t} \sin (\ln t) d t$ ve $g (x) = \int_{1}^{e^{t}} \cos (\ln t) d t$ olmak ūzere $f (\frac{π}{2}) + g (\frac{π}{2})$ toplaminı bulunuz
7) $\int_{- π}^{π} | \cos^{3} x | d x$ integralini hesaplayınz
8) $\int \frac{d x}{\sqrt{- x^{2} + 4 x + 5}}$ integralini hesaplayinı.

Answer

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Answer

$\int \frac{d x}{\sqrt{- x^{2} + 4 x + 5}}$

Steps

Step 1 ： $\int \frac{\sin x}{\cos^{7} x} d x = \int \sin x \cos^{- 7} x d x$

Step 2 ： $\int_{0}^{1} \frac{x \arctan (x^{2})}{1 + x^{4}} d x$

Step 3 ： $\int \cos^{6} x \sin x \tan^{2} x d x$

Step 4 ： $\int \frac{2 x + 5}{x^{3} + 5 x} d x$

Step 5 ： $f (x) = \int_{1}^{t} \sin (\ln t) d t$ ; $g (x) = \int_{1}^{e^{t}} \cos (\ln t) d t$ ; $f (\frac{π}{2}) + g (\frac{π}{2})$

Step 6 ： $\int_{- π}^{π} | \cos^{3} x | d x$

Step 7 ： $\int \frac{d x}{\sqrt{- x^{2} + 4 x + 5}}$